
#REDIRECT Quantum mechanics
:Quantum mechanics has provoked a strong philosophical debate. The fundamental problem is that causality and determinism is lost: while the probability distributions evolve according to a well established deterministic law, the values of the observables themselves do not. Because of this, Albert Einstein held that quantum mechanics must be incomplete. It would be helpful to try to give some basic explanation of ''why'' Einstein's view is widely held to be incorrect--his view seems like common sense, but common sense is often wrong, as theoretical physicists enjoy pointing out. So, why is it wrong, in this case? By the way, please don't answer this question on the talk:Quantum_Mechanics page--please put the answer on the QM page. Thanks in advance! --User:LMS It's not entirely clear that Einstein was wrong on all counts, just wrong on at least one of them. :-) The Bell's-inequality experiments of Aspect prove beyond any doubt that either (1) Observable effects exist that cannot be deterministic results of inherent properties of matter; or (2) The universe is non-local; i.e., physical effects can propogate faster than light. Nobody knows which. --LDC It proves neither, since neither is the case in the multi-universe interpretation. --User:Josh Grosse I'll put a discussion of these issues on the :Copenhagen interpretation page. --AxelBoldt ---- In the "Description of the theory" section, it states that the view of the electron circling a protron was replaced by the view of a static "probability cloud". However, this gives the misleading interpretation of the electron as being "smeared" in some distribution around the proton, which isn't really case. The electron does in fact move around the proton, we are just unable to predict the nature of this movement and can only predict the probability of finding the electron in any given location. That the electron is not "smeared" throughout the distribution, but occupies unique points in space is evidenced by the relative inaccuracy of the Hartree-Fock approximation compared to Density Functional Theory or other methods that attempt to account for the "correlation energy" that arises due to the interactions between moving electrons. --User:Matt Stoker Current understanding is that the electron is smeared. If a wave function was just a probability distribution for a particle that actually had a given position, the double-slit experiment wouldn't work, since the electron would have to travel through one slit or the other. I'll admit to not knowing precisely how correlation energy works, but absolutely none of the fundamental quantum mechanics I have seen treats orbitals as anything other than stationary states. --User:Josh Grosse The electron cannot be smeared over the orbitial, since if it were then the electric field would also be smeared. This smeared view of the electric field is the limiting assumption in the Hartree-Fock approximation and is the reason for it's limited applicability to multi-electron systems. The electric field cannot be treated in an average or smeared fashion because electrons repulse each other, this repulsion results in an instantaneous distortion of the probability distribution for a given electron that depends on the instantaneous position of the other electrons at any given point in time. The difference between the exact energy and the Hartree-Fock energy due to these instantaneous electron interactions is called the "correlation energy". My understanding is that modifications of the double-slit experiment were performed in which the researchers attempted to detect which slit the electron passed through. In these experiments, they were able to determine which slit each electron passed through, but the measurements perturbed the system, such that the typical diffraction patern did not occur. In other words, when the electron was detected as a particle with a definite position, the system behaved as if the electron were a particle. The wave function collapsed, because the electron position was detected. I would imagine that the interactions between electrons are similar. Instantaneous interactions between electrons cause the wave functions to collapse, so at any given time the electrons "see" the other electrons with a unique position and the electric field corresponds to specific electron positions. --Matt Stoker But electrons are always interacting with other electrons, so if this was enough to collapse the wave function, you could never have an electron in two places at once. What happens when two electrons interact is that their wave functions become ''entangled'', and that's where the correlation comes from, although I don't know the mathematical details. In the copenhagen interpretation, you need a real observer to cause collapse, while in the many-worlds interpretation, collapse does not occur at all (only entanglement between the system and observer). --JG When I wrote the sentence about static electron probability clouds, I did not have "smeared out electrons" in mind; rather, I thought about a probability distribution that tells you how likely it is to find the electron at a given point, the electron being a particle, not a cloud. Maybe I should clarify that somehow? Any suggestions? Also, we have some treatment of the double-slit experiment in :Wave-Particle duality. Let me know if that is inaccurate. --AxelBoldt Request to leave the sentence alone. In copenhagen electrons are clouds until observed - that's what wave-particle duality is all about - and in other interpretations they are clouds period. Actually there's no conflict between having an electron "smeared out" and it having a velocity (~momentum). Since the electron is described by a wave(function) it can (and will) do both at the same time. The prime example here is a free electron. If a free electron has an exactly determined momentum its wavefunction will be spread out evenly over whole space (maybe a rather theoretical example..). Actually the electrons around a nucleus also both have a momentum and are delocalized (and you can solve the Shrödinger equation for Hydrogen exactly). Even if you go from Hartree-Fock to Full CI (Which is a method to solve the Schrödinger equation exactly within a finite basis-set) you still get delocalized electrons. -- Ulf Ekström
[[Image:HAtomOrbitals.png|thumb|275px|Fig. 1: The wavefunctions of an electron in a hydrogen atom possessing definite energy (increasing downward: ''n''=1,2,3,...) and angular momentum (increasing across: ''s'', ''p'', ''d'',...). Brighter areas correspond to higher probability density for a position measurement. The angular momentum and energy are quantization (physics), and only take on discrete values like those shown.]] Quantum mechanics is a fundamental physical theory which extends and corrects classical mechanics, especially at the atomic and subatomic particle levels. It is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. The term ''quantum'' (Latin, "''how much''") refers to the discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). #Description of the theory is a theory of mechanics, a branch of physics that deals with the motion of bodies and associated Quantity such as energy and momentum. It is believed to be a more fundamental theory than Newtonian mechanics, because it provides accuracy and precision descriptions for many physical phenomenon where Newtonian mechanics drastically fails. This includes the behavior of systems at atomic length scales and below — in fact, Newtonian mechanics is unable to account for the existence of stable atoms — as well as special macroscopic systems such as superconductivity and superfluids. The predictions of quantum mechanics have never been falsifiability after a century's worth of experiments. Quantum mechanics incorporates at least three classes of phenomena that classical physics cannot account for: (i) the quantization (physics) (discretization) of certain physical quantities, (ii) wave-particle duality, and (iii) quantum entanglement. In certain physical situations, the laws of quantum mechanics approximate the laws of classical mechanics to a high degree of precision; this is often expressed by saying that quantum mechanics reduces to classical mechanics and is known as the correspondence principle. Quantum mechanics can be formulated in either a theory of relativity or non-relativistic manner. Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known, though non-relativistic quantum mechanics is also frequently used for reasons of convenience. We will use the term "quantum mechanics" to refer to both relativistic and non-relativistic quantum mechanics; the terms quantum physics and quantum theory are synonymous. It should be noted, however, that certain authors refer to "quantum mechanics" in the more restricted sense of non-relativistic quantum mechanics. Most physicists believe that quantum mechanics provides a correct description for the physical world under ''almost'' all circumstances. It seems likely that quantum mechanics fails in the vicinity of black holes, or when considering the observable Universe as a whole. In these regimes, quantum mechanics conflicts with the predictions of general relativity, the dominant theory of gravity. The question of compatibility between quantum mechanics and general relativity remains an area of active research. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born, von Neumann, Paul Dirac, Wolfgang Pauli and List of physicists#Famous physicists of the 20th century. Some fundamental aspects of the theory are still actively studied. == Description of the theory == There are a number of mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly-used formulations is the transformation theory (quantum mechanics) invented by Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). In this formulation, the quantum state encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either Continuous function (e.g., the position of a particle) or discrete (e.g. the energy of an electron bound to a hydrogen atom.) Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as "eigenstates" of the observable ("eigen" meaning "own" in German language). A concrete example will be useful here. Let us consider a free particle. Its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wave function. The position and momentum of the particle are observables. An eigenstate of position is a wavefunction that is very large at a particular position ''x'', and zero everywhere else. If we perform a position measurement on such a wavefunction, we will obtain the result ''x'' with 100% probability. An eigenstate of momentum, on the other hand, has the form of a plane wave. It turns out that the wavelength is equal to ''h/p'', where ''h'' is Planck's constant and ''p'' is the momentum of the eigenstate. Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if we measure the observable, the wavefunction will immediately become an eigenstate of that observable. This process is known as wavefunction collapse. If we know the wavefunction at the instant before the measurement, we will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in our previous example will usually have a wavefunction that is a wave packet centered around some mean position ''x0'', neither an eigenstate of position nor of momentum. When we measure the position of the particle, it is impossible for us to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near ''x0'', where the amplitude of the wavefunction is large. After we perform the measurement, obtaining some result ''x'', the wavefunction collapses into a position eigenstate centered at ''x''. Wave functions can change as time progresses. An equation known as the Schrödinger equation describes how wave functions change in time, a role similar to Newton's second law in classical mechanics. The Schrödinger equation, applied to our free particle, predicts that the center of a wave packet will move through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain. This also has the effect of turning position eigenstates into broadened wave packets that are not position eigenstates. Some wave functions produce probability distributions that are constant in time. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherical coordinate system probability cloud surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum states, labelled ''s'', are spherically symmetric). The time evolution of wave functions is determinism in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a quantum measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e. random. The probability nature of quantum mechanics thus stems from the act of measurement: the object interacts with an apparatus, and their respective wavefunctions become entangled. In effect, the object ceases to exist as an independent entity. This may introduce some uncertainty into the prediction of what the outcome of a measurement may become, at some stage in the future, insofar as this prediction is required to draw information only from the object wavefunction. However, it might be thought that, by preparing the apparatus beforehand, its influence during the measurement might be predictable, or at least afterwards detectable, so that this kind of uncertainty might be merely a matter of insufficient data. But, as it turns out, to actually detect such influence data, by handling the apparatus, is incompatible with its functioning as a measurement device. That is, for practical reasons, the apparatus cannot do both at the same time. It is therefore a matter of principle, rather than practice, that one has the uncertainty which necessitates a probabilistic prediction. This is one of the most difficult ideas to understand about the nature of quantum systems. It was the central topic in the famous Bohr-Einstein debates, in which they sought to clarify these fundamental principles by way of thought experiments. There are some Interpretation_of_quantum_mechanics of quantum mechanics that do away with the concept of "wavefunction collapse" by altering the concept of what constitutes a "measurement" in quantum mechanics. For example, see relative state interpretation. === Quantum mechanical effects === As mentioned in the introduction, there are several classes of phenomena that appear under quantum mechanics which have no analogue in classical physics. These are sometimes referred to as "quantum effects". The first type of quantum effect is the quantization (physics) of certain physical quantities. In the example we have given, of a free particle in empty space, both the position and the momentum are continuous observables. However, if we restrict the particle to a region of space (the so-called "particle in a box" problem), the momentum observable will become discrete; it will only take on the values ''h/L'', where ''L'' is the length of the box. Such observables are said to be Quantization (physics), and they play an important role in many physical systems. Examples of quantized observables include angular momentum, the total energy of a bound system, and the energy contained in an electromagnetic wave of a given frequency. Another quantum effect is the uncertainty principle, which is the phenomenon that consecutive measurements of two or more observables may possess a fundamental limitation on accuracy. In our free particle example, it turns out that it is impossible to find a wavefunction that is an eigenstate of both position and momentum. This implies that position and momentum can never be simultaneously measured with arbitrary precision, even in principle: as the precision of the position measurement improves, the maximum precision of the momentum measurement decreases, and vice versa. Those variables for which it holds (e.g. momentum and position, or energy and time) are Hamiltonian mechanics in classical physics. Another quantum effect is the wave-particle duality. It has been shown that, under certain experimental conditions, microscopic objects like atoms or electrons exhibit particle-like behavior, such as scattering. ("Particle-like" in the sense of an object that can be localized to a particular region of space.) Under other conditions, the same type of objects exhibit wave behavior, such as Wave interference. We can observe only one type of property at a time. Another quantum effect is quantum entanglement. In some cases, the wave function of a system composed of many particles cannot be separated into independent wave functions, one for each particle. In that case, the particles are said to be "entangled". If quantum mechanics is correct, entangled particles can display remarkable and counter-intuitive properties. For example, a measurement made on one particle can produce, through the collapse of the total wavefunction, an instantaneous effect on other particles with which it is entangled, even if they are far apart. This only appears to conflict with special relativity. There is no transmission of information in the process, which would require a physical object to move (instantaneously) between the two particles. It is only by coming together, at some later meeting, that the two investigators can compare their data, and detect the remarkable correlations they contain. === Mathematical formulation === ''Main article: Mathematical formulation of quantum mechanics. See also the discussion in Quantum logic.'' In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex number Separable space Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system.) The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single electron is just the product of two complex planes. Each observable is represented by a densely-defined Hermitian (or self-adjoint operator) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues. The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (quantum mechanics), the Operator (physics) corresponding to the total energy of the system, generates time evolution. The inner product between two state vectors is a complex number known as a probability amplitude. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of ''Hermitian'' operators, for which all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing the spectral theorem of the corresponding operator. Heisenberg's uncertainty principle is represented by the statement that the operators corresponding to certain observables do not Commutator. The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the wave-like behavior of quantum states. It turns out that analytic solutions of Schrödinger's equation are only available for a small number of model Hamiltonians, of which the quantum harmonic oscillator and the hydrogen atom are the most important representatives. Even the helium atom, which contains just one more electron than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory (quantum mechanics) one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak potential energy. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of quantum chaos. An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics. ===Interactions with other scientific theories=== The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical physics when a system becomes large. This "large system" limit is known as the ''classical'' or ''correspondence limit''. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit. When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was theory of relativity classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the harmonic oscillator. Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field rather than a fixed set of particles. The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetism. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed since the inception of quantum mechanics, is to treat electric charge particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical ''1/r'' Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles. Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the subnuclear particles: quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory known as electroweak force. It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity. ==Applications of quantum theory== Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behavior of the microscopic particles that make up all forms of matter - electrons, protons, neutrons, and so forth - can often only be satisfactorily described using quantum mechanics. Quantum mechanics is important for understanding how individual atoms combine to form chemicals. The application of quantum mechanics to chemistry is known as quantum chemistry. Quantum mechanics can provide quantitative insight into chemical bonding processes by explicitly showing which molecules are energetically favorable to which others, and by approximately how much. Most of the calculations performed in computational chemistry rely on quantum mechanics. Much of modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and Magnetic Resonance Imaging. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics. Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum states over arbitrary distances. == Philosophical consequences == Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophy debate and many interpretations of quantum mechanics. Even fundamental issues such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated. The Copenhagen interpretation, due largely to Niels Bohr, was the standard interpretation of quantum mechanics when it was first formulated. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and do not simply reflect our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than Determinism. Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. He held that there should be a local hidden variable theory underlying quantum mechanics and consequently the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the EPR paradox. John Stewart Bell showed that the EPR paradox led to experimentally testable differences between quantum mechanics and local hidden variable theories. Experiments have been taken as confirming that quantum mechanics is correct and the real world cannot be described in terms of such hidden variables. "Bell test loopholes" in the experiments, however, mean the question is still not quite settled. See the Bohr-Einstein debates The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a "multiverse" composed of mostly independent parallel universes. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities because we can observe only the universe we inhabit. The Bohm interpretation, formulated by David Bohm, postulates the existence of a non-local, universal wavefunction (Schrödinger equation) which allows distant particles to interact instantaneously. Based on this interpretation, Bohm has speculated that the ultimate nature of physical reality is not a collection of separate objects (as it appears to us), but rather an undivided whole that is in perpetual dynamic flux. However, the Bohm interpretation is not popular among physicists, largely because it is considered very inelegant. == History == In 1900, Max Planck introduced the idea that energy is quantized, in order to derive a formula for the observed frequency dependence of the energy emitted by a black body. In 1905, Einstein explained the photoelectric effect by postulating that light energy comes in quanta called photons. In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization. In 1924, Louis-Victor de Broglie put forward his theory of matter waves. These theories, though successful, were strictly phenomenology (science): there was no rigorous justification for quantization. They are collectively known as the ''old quantum theory''. The phrase "quantum physics" was first used in Johnston's ''Planck's Universe in Light of Modern Physics''. Modern quantum mechanics was born in 1925, when Werner Heisenberg developed matrix mechanics and Erwin Schrödinger invented wave mechanics and the Schrödinger equation. Schrödinger subsequently showed that the two approaches were equivalent. Heisenberg formulated his uncertainty principle in 1927, and the Copenhagen interpretation took shape at about the same time. Starting around 1927, Paul Dirac unified quantum mechanics with special relativity. He also pioneered the use of operator theory, including the influential bra-ket notation, as described in his famous 1930 textbook. During the same period, John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period still stand, and remain widely used. The field of quantum chemistry was pioneered by Walter Heitler and Fritz London, who published a study of the covalent bond of the hydrogen molecule in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American chemist Linus Pauling. Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than single particles, resulting in what are known as Quantum field theory. Early workers in this area included Paul Dirac, Wolfgang Pauli, Victor Weisskopf, and Pascaul Jordan. This area of research culminated in the formulation of quantum electrodynamics by Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro Tomonaga during the 1940s. Quantum electrodynamics is a quantum theory of electrons, positrons, and the electromagnetic field, and served as a role model for subsequent quantum field theories. The many worlds interpretation was formulated by Hugh Everett in 1956. The theory of quantum chromodynamics was formulated beginning in the early 1960s. The theory as we know it today was formulated by Politzer, Gross and Wilzcek in 1975. Building on pioneering work by Schwinger, Peter Higgs, Goldstone and others, Sheldon Lee Glashow, Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. ===Founding experiments=== * Thomas Young (scientist)'s double-slit experiment proving the wave nature of light (c1805) * Henri Becquerel discovers radioactivity (1896) * Joseph John Thomson's cathode ray tube experiments (discovers the electron and its negative charge) (1897) * The study of black body radiation between 1850 and 1900, which could not be explained without quantum concepts. * The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy * Robert Millikan's oil-drop experiment, which showed that electric charge occurs as ''quantum'' (whole units), (1909) * Ernest Rutherford's gold foil experiment disproved the plum pudding model of the atom which suggested that the positive charge and mass of the atom are almost uniformly distributed. (1911) * Otto Stern and Walter Gerlach conduct the Stern-Gerlach experiment, which demonstrates the quantized nature of particle Spin (physics) (1920) * Clinton Davisson and Lester Germer demonstrate the wave nature of the electron (1927) *Clyde L. Cowan and Frederick Reines confirm the existence of the neutrino in the neutrino experiment (1955) == See also == * Quantum electrochemistry * Quantum information * Measurement in quantum mechanics == References == * Mackey, George Whitelaw (2004). ''The mathematical foundations of quantum mechanics''. Dover Publications. ISBN 0486435172. ==Notes== *[http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html The Davisson-Germer experiment, which demonstrates the wave nature of the electron] == External links == *[http://plato.stanford.edu/entries/qm Quantum Mechanics (''Stanford Encyclopedia of Philosophy'')] *[http://www.mtnmath.com/faq/meas-qm.html Quantum mechanics] *[http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics] *[http://www.physicstoday.org/pt/vol-54/iss-2/p11.html David Mermin on the future directions of physics] *[http://www.decoherence.de New developments in the understanding of the quantum-classical relation] *[http://higgo.com/quantum/laymans.htm A Lazy Layman's Guide to Quantum Physics] *[http://www.thch.uni-bonn.de/tc/people/brems.vincent/vincent/faq.html A short FAQ on quantum resonances] Quantum mechanics lv:Kvantu mehānika vi:Cơ học lượng tử
---- Discussion archives: /Archive1 – /Archive2 (2004) ---- ==Experimental confirmation of predictions== As it stands, experimental confirmation of the theory seems to be mentioned only within the "philosophical consequences" section, where it crops up in relation to the Bell tests and entanglement. Perhaps "Experimental confirmation" should be a section of its own? User:Caroline Thompson 17:14, 14 Jan 2005 (UTC) :I suggest a separate article; otherwise , too much in one article. ==wording quibble== "Quantum mechanics is a physical theory which, for very small objects such as atoms, produces results that are very different and much more accurate than those of classical mechanic" First, it's not just small things, there are macroscopic q. phenomena, eg superconductivity/fluidity/lasers blackbody radiation spectra, heat content of solids, etc ; and it's not that for atoms it provides a more accurate theroy than classical mech, it's that classical mech. doesn't provide ANY theory that's EVEN CLOSE to the facts, for atoms, and those other things I just mentioned. Needs rewriting.User:67.118.116.145 04:38, 21 Jan 2005 (UTC) :I agree with your points. I made an attempt to address them. Tell me what you think. -User:Lethe | User talk:Lethe 05:14, Jan 21, 2005 (UTC) == Gnome!? == In a recent edit, someone added a picture of a garden gnome and nothing else. I could just be missing some obvious connection between gnomes and quantum mechanics, but I doubt it. I'm removing it for the moment. ==Feynman== Richard Feynman was not among the founding fathers of QM. I added Pauli's name there instead.--User:Ashujo Feb 11, 2005 == More founding experiments? == Doesn't the line spectra of atomic hydrogen hold its place among the ones mentioned? I am from Sweden so I might be biase to Rydberg, but I guess Bohr migh side with me on this... Maybe also the photo-ekectric effect - connecting Plank's constant with something else than the black-bodies? == more fundamental theory == User:CYD, I noticed that you removed my remark about quantum mechanics being suitable a more fundamental theory. Didn't you like it? Basically, I have in mind that any theory with the larger domain of applicability should be said to be more fundamental. -User:Lethe | User talk:Lethe 08:00, Mar 3, 2005 (UTC) :Okay, now I see what you are getting at. I put it back in a slightly different form. -- User:CYD == new intro == I have some comments about the new intro: # I like the idea of the new intro. It would be useful to put quantum mechanics into the larger context of other kinds of mechanics. # but don't just insert a new intro in front of the existing intro # respect the conventions of the article. For example, this article uses the phrase "quantum mechanics" to mean any theory that is quantized. Therefore, to distinguish quantum mechanics from relativistic quantum mechanics is confusing. # furthermore, I would not seperate relativistic quantum mechanics from nonrelativistic quantum mechanics. The only difference between the two is basically a choice of Hamiltonian. # quantum field theory, on the other hand, is the true marriage of quantum mechanics and relativity. And it is a qualitatively different theory from quantum mechanics (single particle). # what you consider to be a significant fraction of the speed of light depends of course on your needs. GPS satellites probably don't even go 0.1% the speed of light, but still the engineers use relativistic mechanics with them. Because they require great accuracy. # we changed in the old intro some wording to make clear that it's not the smallness that makes quantum mechanics apply. Some atoms are classical, and some macroscopic systems are quantum. So it's inaccurate to just say "small things like atoms" are quantum systems. and again, it depends on the level of accuracy. #Classical mechanics includes many things besides Newtonian mechanics. I would distinguish Hamiltonian and Lagrangian mechanics from Newtonian mechanics. I might also distinguish fluid mechanics, statistical mechanics. # what about general relativity? Shouldn't it fit in some where? -User:Lethe | User talk:Lethe 23:40, Apr 13, 2005 (UTC) : :To make the article less tedious, how about moving the first five paragraphs elsewhere to other articles in the physics category? This preliminary non-quantum prose might even be a welcome addition to a section of the major physics article. The state of the article when it had just become featured was pretty good. Right now, a re-run of other topics makes for tedious reading. There isn't an equation in sight, for some reason. User:Ancheta Wis 00:38, 14 Apr 2005 (UTC) My thanks to LauraScudder for the improvements as I was typing this. :As of 08:36, 14 Apr 2005 (UTC), the first paragraph belongs to a parent article. My vote is to move it to physics or mechanics. User:Ancheta Wis 08:36, 14 Apr 2005 (UTC) :The new intro has got us arguing over whether Newtonian mechanics is all there is to classical mechanics and I've been editing such things too until I realized that the subfields of classical mechanics have nothing to do with quantum mechanics and just distract and confuse the unintiated while boring the others. I shortened that segment to: ::''Most physicists would divide mechanics into four major areas: classical mechanics, Theory of relativity mechanics, and quantum mechanics. ::But in physics, quantum mechanics can be regarded as ''the'' fundamental theory. '' :I think it simplifies the intro significantly and takes it back to the spirit of the first featured version while still putting the field into context for those who want to clicky clicky like mad. The distinction between nonrelativistic quantum mechanics and relativistic quantum field theory is made on the appropriate quantum field theory pages.--User:Laurascudder 18:28, 14 Apr 2005 (UTC) == Introduction == You are losing our reader with this introduction, although the worst was taken care of during the last few days. Please consider the frame-of-mind of someone seeking info on "quantum mechanics" as a fairly unfamiliar topic. This reader does not want to hear about Newtonian mechanics, or relativity, or any number of other fancy classifications, at least not until later. Give the reader a break, at plainly start by telling what it is about. And why anyone should take an interest, besides the specialists. April 15, 2005 - Guest :I agree, in making the introduction more "accessible", we have severely bogged it down. Also doesn't really match the Wikipedia:WikiProject Science guidelines now either. I'll be bold and if people disagree, edit away and/or discuss here. --User:Laurascudder 18:13, 14 Apr 2005 (UTC) ::Yes, much nicer. However, I have to say that "relativistic" should not be extracted from either classical or quantum mechanics. Both include relativity (special, of course), and one takes a non-relativistic limit as the need arises. I know that most university course plans start out non-relativistically, and this should of course be mentioned, and is quite reasonable, but it is not really fundamental. We don't hit students with relativity on day one, of course (we wait a couple of months:-). Also, something must be done for the general readers, there has got to be many at this place, and they should be able to come away with something too. -Guest April 15, 2005 It appears you are advocating the position of a reader who has not yet considered the microcosm. This suggests that the article might start off with the atomic hypothesis, then radioactive decay, or perhaps cosmic rays (leakage from a Leyden jar, etc.). ... This approach might then culminate with the statement about general applicability of QM as a fundamental theory, and the current non-relationship to GR. A complete rewrite or new article history of quantum mechanics. User:Ancheta Wis 10:32, 15 Apr 2005 (UTC) ( By the way, you can date-time-stamp your posts with the 5-tilde notation:~~~~~ )
:Well, yes and no, advocating "the position of a reader that has not yet considered the microcosm". Of course, the large scale history as you describe it belongs elsewhere. However, as anyone who teaches (science not least) will confirm, it is very easy to assume too much pre-knowledge, and not advisable. In a *pedia one really should be forthcoming towards uninitiated readers, at least when dealing with a difficult topic (if ever there was one) which receives much public attention. For instance, consider the general use of the term "theory" as some sort of idle speculation, while quantum theory is often presented in the media as a collection of "puzzles and paradoxes". It ought to be clearly stated up front how most serious an enterprise it really is.
:Here is what I had in mind - hope I managed to incorporate your latest contributions. It would perhaps be fair of me to let you know a little of my background, but on the other hand, it's the words that count, so maybe better to do without. -Guest April 15, 2005
Umm, no. An introduction has to introduce the topic clearly and concisely. ''Quantum mechanics is regarded by virtually all physicists as the most fundamental framework currently available for understanding physical nature (but it is not the only one in use)'' is a terrible way to start an article. -- User:CYD
:I can assure it is true, and what people want to be sure of when paying tuition - but suit yourself. -Guest April 15, 2005
:Let me elaborate on that sentiment. I think, Guest, that you're trying to do an admirable thing by making this article more accessible to the unititiated, especially since it has become featured, but are going about it the wrong way. For someone who doesn't understand the distinctions between fields of physics well, the most important thing to know right off the bat is that quantum mechanics means quantization and that it's the best theory we've got right now (argue that one with the string theorists).
:According to Wikipedia:WikiProject Science guidelines, we do need to put it into context, but too much context is just making distinctions the newcomer doesn't understand (quantum physics versus quantum mechanics versus quantum field theory - not to mention that I disagree that studying fields is outside of mechanics) while boring the experienced. I think saying its the best theory we've got and has some mindbending consequences (wave-particle duality) is a pretty good motivation take an interest in it. --User:Laurascudder | User talk:Laurascudder 16:42, 15 Apr 2005 (UTC)
::It's the centuries-old question: my kid would do well to become a lawyer or a doctor, but he/she wants to be a physicist (it used to be astronomer) - but that's all up-in-the-air, or isn't it? When coming to an article like this, the reader is entitled to a clear and unambigous statement, of what this subject means in the world, and not to go directly into some jargon for the initiated. As a professional physicst, who has taught quantum mechanics to those kids for a long time, I know very well that the point is quantization, but that makes no sense at all outside of physics. First question to answer: is it any good?
And by the way, from your quotes it seems like you're not looking at my version - which was the "soft learning curve" one. -Guest April 15, 2005
:Thank you for your thoughts on the intro. Here is my take on your 4-paragraph precis of QM:
#QM is a fundamental framework for understanding Nature. It has withstood a century of experimentation, and therefore is worth your intellectual investment required to learn it (as the student).
#QM applications and successes.
#QM has some surprises for anyone wishing to invest time learning it.
#as for QM vs GR, the story is not complete yet; there is hope that you (the student) can add to the physics, should you care to accept the challenge.
:I do not disagree that the 4-part story is intriguing. The English is immaterial and can be word-smithed if everyone is agreeable that the 4-part structure (+the 5th para. of names) makes a good intro. I like what I see. User:Ancheta Wis 02:25, 16 Apr 2005 (UTC)
::Now if I may, Prof. G., ask you some questions: The Schrödinger picture is really how I think of the topic, based on my brainwashed view of the flow of time, but I am told that Dirac espoused the Heisenberg picture; it takes an odd frame of mind to view the system using time as an independent variable upon which we can travel at will. I have to admit difficulty visualizing such a system. But if we take a GR POV, and view the cosmos as evolving in time and space, much like a tree growing, I can visualize that. Might it be possible that the Heisenberg picture is more like GR (or statistical mechanics) that way? That would give me more of a feel for the evolution operator. So right away, the framework aspect of QM comes up for explication and evaluation. (Your paragraph 1 of the intro) It's difficult, in another way. Unless the student can take that on faith, somehow. It's like the student has to start all over again, on another kind of kinematics. I would imagine that the dropout rate would be high, to get through the framework part. That implies that the successes (paragraph 2) are what sustains the student. User:Ancheta Wis 02:25, 16 Apr 2005 (UTC) Yet upon reflection, to state that the framework is the general entry point for learning QM, has to be a ''conclusion'' based on the century of development and experimentation; QM certainly didn't start out with that status at all. So the 4 part intro can't be the TOC for an article or course, it would have to start with experiment, perhaps a failed hypothesis or two, and then the string of successes.
::Another line of questioning: QM is the basis for computational chemistry, which takes up a ton of computing power. Yet we do not hear much about the codes currently in use by Peter Coveney et. al. I would think that your students could gain some significant experience if they got some background for that area. I still am unclear on how much the QM computer codes compare in processing load, compared say to Earth Simulator.
::I recognize that the questions are unfair, but it doesn't hurt to ask. Maybe we can find some answers. User:Ancheta Wis 02:25, 16 Apr 2005 (UTC)
Umm, most of this is dealt with in the rest of the article, if one bothers to read anything apart from the introduction. See, in particular, the section ''Interactions with other scientific theories''. See also Wikipedia:Manual of Style#Introduction. -- User:CYD
Reply to Ancheta Wis: Thanks for taking time with my suggested intro (which is at "intro with softer learning curve" [http://en.wikipedia.org/w/index.php?title=Quantum_mechanics&oldid=12345900 here]>; it was immediately thrown out by CYD).
Just passing by as a guest, I got somewhat disturbed at the impression an uninitiated reader of this featured article would get. Science is not faring too well among young people, and I find that it is partly due to the way it gets represented in the media: too much nerdy whizzkid, too little serious business. Choosing a line of study, we all need to see the long professional aspect, not just the instant gratification entertainment value. Therefore I find it important to provide a readable and understandable intro, where the reader can hang on as long as possible. I'm pleased to see that you recognize this.
My contribution is/was an attempt to simplify the flow of ideas, which seemed to me to have gotten rather entangled (with all due respect, probably an artefact of the editing procedure). As we all know, of course, to start a fresh version can often help.
Here are my answers to your (welcome) questions (and some thoughts while we're at it):
> QM is a fundamental framework for understanding Nature. It has withstood a century of experimentation, and therefore is worth your intellectual investment required to learn it (as the student).
Indeed, and your financial investment too (as a parent). As a community, physicists can assert this in absolute honesty, and with complete confidence. The scientific test procedures involved in that so many physicists have worked on this, everywhere, every day, for a hundred years, is so tremendous that it needs to be asserted explicitly. No one outside science or technology can possibly have any realistic idea of the degree of certainty that has been achieved here. Now, I am well aware, of course, that as an academic one tends to shy away from making such blunt statements - and that's why it's not well understood outside of science. Now, since practically every professional physicist (and chemist as well, I suppose) agrees, I believe it should be said here, in this article, in an unambigous statement, that, this is what most of us find, and that many of us use quantum mechanics day in and day out (except, of course, ... you know). It does not have to be presented as an absolute and final truth (which no physicist of course would subscribe to), but the strong confidence must come through. It is justified.
> QM applications and successes.
Yes, most readers will appreciate this when listed in general terms. And I linked to the quantum specific pages.
> QM has some surprises for anyone wishing to invest time learning it.
Now that we have said that quantum mechanics is serious, and works, it's motivating to know this.
> as for QM vs GR, the story is not complete yet; there is hope that you (the student) can add to the physics, should you care to accept the challenge.
Yes, we really hope that one of you (students) will be the one to make a discovery, like what Planck did, to find the more fundamental framework of the future.
> I do not disagree that the 4-part story is intriguing. The English is immaterial and can be word-smithed if everyone is agreeable that the 4-part structure (+the 5th para. of names) makes a good intro. I like what I see. Ancheta Wis 02:25, 16 Apr 2005 (UTC)
Thanks.
> Now if I may, Prof. G., ask you some questions: The Schrödinger picture is really how I think of the topic, based on my brainwashed view of the flow of time, but I am told that Dirac espoused the Heisenberg picture; it takes an odd frame of mind to view the system using time as an independent variable upon which we can travel at will. I have to admit difficulty visualizing such a system. But if we take a GR POV, and view the cosmos as evolving in time and space, much like a tree growing, I can visualize that. Might it be possible that the Heisenberg picture is more like GR (or statistical mechanics) that way? That would give me more of a feel for the evolution operator. So right away, the framework aspect of QM comes up for explication and evaluation. (Your paragraph 1 of the intro)
As you know, the Heisenberg picture is mathematically and physically equivalent to the Schrödinger picture, by unitary transformation. It is good for theoretical work, and is quite widely used. For visualization, I recommend using the H picture with the Ehrenfest procedure, to recover the Newton equations of motion, where the time dependence nicely associates with the observables, as we are used to. Indeed, in this way I derive classical relativistic electrodynamics, for the (graduate) students in relativistic quantum mechanics, so it is basically all there.
> It's difficult, in another way. Unless the student can take that on faith, somehow. It's like the student has to start all over again, on another kind of kinematics. I would imagine that the dropout rate would be high, to get through the framework part. That implies that the successes (paragraph 2) are what sustains the student. Ancheta Wis 02:25, 16 Apr 2005 (UTC)
Yes, we wait until the second year to do q.m., but in principle one could start with it, in principle. If systematically presented it is not hard to understand, but the mathematical framework must be taught in mathematics beforehand. Many students, of course, are more interested in other things, and just need to see a bit of it, at some stage, to be convinced that it works, and understand how material properties get deduced in q.m. Some day we may even be able to compute masses, some day...
> Yet upon reflection, to state that the framework is the general entry point for learning QM, has to be a conclusion based on the century of development and experimentation; QM certainly didn't start out with that status at all. So the 4 part intro can't be the TOC for an article or course, it would have to start with experiment, perhaps a failed hypothesis or two, and then the string of successes.
Indeed, so we should imply these empirical foundations via the Part 2. Anyhow, It still helps to know that there is a reliable mathematical framework, even if you do not intend to become a specialist in it. So the general framework part is important for building confidence, although the learning is done via more specialized calculus formulations. Hope I understood your question here.
> Another line of questioning: QM is the basis for computational chemistry, which takes up a ton of computing power. Yet we do not hear much about the codes currently in use by Peter Coveney et. al. I would think that your students could gain some significant experience if they got some background for that area. I still am unclear on how much the QM computer codes compare in processing load, compared say to Earth Simulator.
This topic is beyond my scope, so I have to pass on that.
> I recognize that the questions are unfair, but it doesn't hurt to ask. Maybe we can find some answers. Ancheta Wis 02:25, 16 Apr 2005 (UTC)
Not at all. Let's hope it becomes possible to have an introduction that part of the way, at least, makes sense to all readers. -Guest April 16, 2005
== Navbox ==
In order to make the quantum-theory Navbox more accessible in the other articles, I propose that it move up just under a heading, such as Quantum mechanics#Quantum mechanical effects. Thus by inserting a parenthetical link ''([other articles on QM])'' in the child articles, the Navbox becomes more accessible other places. Is that alright with everyone? Alternatively, smaller versions of the quantum-theory Navbox might be placed in the child articles; as its transclusion would overwhelm many of them, currently. User:Ancheta Wis 08:25, 19 Apr 2005 (UTC) As it turns out, the first article I had chosen , on the commutation relation, did not have a link back to QM, so I inserted a small version of the Navbox there. The other articles appear to at least mention this page, so the need for a link to the Navbox is partially answered already. The little navbox is titled
Quantum mechanics (also called quantum physics or quantum theory) is a physics theory that is believed to be the formalism underlying the description of all physical systems. Quantum mechanical departures from classical physics are most often encountered at small length scales, low energies and/or low temperatures. Physics Mechanics Physical chemistry vi:Category:Cơ học lượng tử
See other meanings of words starting from letter:A | B | C | C | D | E | F | G | H | I | J | K | L | M | N | O | P | R | S | T | U | V | X | Y | Z |
Quantum Mechanics
#REDIRECT Quantum mechanics
Quantum Mechanics
:Quantum mechanics has provoked a strong philosophical debate. The fundamental problem is that causality and determinism is lost: while the probability distributions evolve according to a well established deterministic law, the values of the observables themselves do not. Because of this, Albert Einstein held that quantum mechanics must be incomplete. It would be helpful to try to give some basic explanation of ''why'' Einstein's view is widely held to be incorrect--his view seems like common sense, but common sense is often wrong, as theoretical physicists enjoy pointing out. So, why is it wrong, in this case? By the way, please don't answer this question on the talk:Quantum_Mechanics page--please put the answer on the QM page. Thanks in advance! --User:LMS It's not entirely clear that Einstein was wrong on all counts, just wrong on at least one of them. :-) The Bell's-inequality experiments of Aspect prove beyond any doubt that either (1) Observable effects exist that cannot be deterministic results of inherent properties of matter; or (2) The universe is non-local; i.e., physical effects can propogate faster than light. Nobody knows which. --LDC It proves neither, since neither is the case in the multi-universe interpretation. --User:Josh Grosse I'll put a discussion of these issues on the :Copenhagen interpretation page. --AxelBoldt ---- In the "Description of the theory" section, it states that the view of the electron circling a protron was replaced by the view of a static "probability cloud". However, this gives the misleading interpretation of the electron as being "smeared" in some distribution around the proton, which isn't really case. The electron does in fact move around the proton, we are just unable to predict the nature of this movement and can only predict the probability of finding the electron in any given location. That the electron is not "smeared" throughout the distribution, but occupies unique points in space is evidenced by the relative inaccuracy of the Hartree-Fock approximation compared to Density Functional Theory or other methods that attempt to account for the "correlation energy" that arises due to the interactions between moving electrons. --User:Matt Stoker Current understanding is that the electron is smeared. If a wave function was just a probability distribution for a particle that actually had a given position, the double-slit experiment wouldn't work, since the electron would have to travel through one slit or the other. I'll admit to not knowing precisely how correlation energy works, but absolutely none of the fundamental quantum mechanics I have seen treats orbitals as anything other than stationary states. --User:Josh Grosse The electron cannot be smeared over the orbitial, since if it were then the electric field would also be smeared. This smeared view of the electric field is the limiting assumption in the Hartree-Fock approximation and is the reason for it's limited applicability to multi-electron systems. The electric field cannot be treated in an average or smeared fashion because electrons repulse each other, this repulsion results in an instantaneous distortion of the probability distribution for a given electron that depends on the instantaneous position of the other electrons at any given point in time. The difference between the exact energy and the Hartree-Fock energy due to these instantaneous electron interactions is called the "correlation energy". My understanding is that modifications of the double-slit experiment were performed in which the researchers attempted to detect which slit the electron passed through. In these experiments, they were able to determine which slit each electron passed through, but the measurements perturbed the system, such that the typical diffraction patern did not occur. In other words, when the electron was detected as a particle with a definite position, the system behaved as if the electron were a particle. The wave function collapsed, because the electron position was detected. I would imagine that the interactions between electrons are similar. Instantaneous interactions between electrons cause the wave functions to collapse, so at any given time the electrons "see" the other electrons with a unique position and the electric field corresponds to specific electron positions. --Matt Stoker But electrons are always interacting with other electrons, so if this was enough to collapse the wave function, you could never have an electron in two places at once. What happens when two electrons interact is that their wave functions become ''entangled'', and that's where the correlation comes from, although I don't know the mathematical details. In the copenhagen interpretation, you need a real observer to cause collapse, while in the many-worlds interpretation, collapse does not occur at all (only entanglement between the system and observer). --JG When I wrote the sentence about static electron probability clouds, I did not have "smeared out electrons" in mind; rather, I thought about a probability distribution that tells you how likely it is to find the electron at a given point, the electron being a particle, not a cloud. Maybe I should clarify that somehow? Any suggestions? Also, we have some treatment of the double-slit experiment in :Wave-Particle duality. Let me know if that is inaccurate. --AxelBoldt Request to leave the sentence alone. In copenhagen electrons are clouds until observed - that's what wave-particle duality is all about - and in other interpretations they are clouds period. Actually there's no conflict between having an electron "smeared out" and it having a velocity (~momentum). Since the electron is described by a wave(function) it can (and will) do both at the same time. The prime example here is a free electron. If a free electron has an exactly determined momentum its wavefunction will be spread out evenly over whole space (maybe a rather theoretical example..). Actually the electrons around a nucleus also both have a momentum and are delocalized (and you can solve the Shrödinger equation for Hydrogen exactly). Even if you go from Hartree-Fock to Full CI (Which is a method to solve the Schrödinger equation exactly within a finite basis-set) you still get delocalized electrons. -- Ulf Ekström
Quantum mechanics
[[Image:HAtomOrbitals.png|thumb|275px|Fig. 1: The wavefunctions of an electron in a hydrogen atom possessing definite energy (increasing downward: ''n''=1,2,3,...) and angular momentum (increasing across: ''s'', ''p'', ''d'',...). Brighter areas correspond to higher probability density for a position measurement. The angular momentum and energy are quantization (physics), and only take on discrete values like those shown.]] Quantum mechanics is a fundamental physical theory which extends and corrects classical mechanics, especially at the atomic and subatomic particle levels. It is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. The term ''quantum'' (Latin, "''how much''") refers to the discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). #Description of the theory is a theory of mechanics, a branch of physics that deals with the motion of bodies and associated Quantity such as energy and momentum. It is believed to be a more fundamental theory than Newtonian mechanics, because it provides accuracy and precision descriptions for many physical phenomenon where Newtonian mechanics drastically fails. This includes the behavior of systems at atomic length scales and below — in fact, Newtonian mechanics is unable to account for the existence of stable atoms — as well as special macroscopic systems such as superconductivity and superfluids. The predictions of quantum mechanics have never been falsifiability after a century's worth of experiments. Quantum mechanics incorporates at least three classes of phenomena that classical physics cannot account for: (i) the quantization (physics) (discretization) of certain physical quantities, (ii) wave-particle duality, and (iii) quantum entanglement. In certain physical situations, the laws of quantum mechanics approximate the laws of classical mechanics to a high degree of precision; this is often expressed by saying that quantum mechanics reduces to classical mechanics and is known as the correspondence principle. Quantum mechanics can be formulated in either a theory of relativity or non-relativistic manner. Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known, though non-relativistic quantum mechanics is also frequently used for reasons of convenience. We will use the term "quantum mechanics" to refer to both relativistic and non-relativistic quantum mechanics; the terms quantum physics and quantum theory are synonymous. It should be noted, however, that certain authors refer to "quantum mechanics" in the more restricted sense of non-relativistic quantum mechanics. Most physicists believe that quantum mechanics provides a correct description for the physical world under ''almost'' all circumstances. It seems likely that quantum mechanics fails in the vicinity of black holes, or when considering the observable Universe as a whole. In these regimes, quantum mechanics conflicts with the predictions of general relativity, the dominant theory of gravity. The question of compatibility between quantum mechanics and general relativity remains an area of active research. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born, von Neumann, Paul Dirac, Wolfgang Pauli and List of physicists#Famous physicists of the 20th century. Some fundamental aspects of the theory are still actively studied. == Description of the theory == There are a number of mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly-used formulations is the transformation theory (quantum mechanics) invented by Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). In this formulation, the quantum state encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either Continuous function (e.g., the position of a particle) or discrete (e.g. the energy of an electron bound to a hydrogen atom.) Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as "eigenstates" of the observable ("eigen" meaning "own" in German language). A concrete example will be useful here. Let us consider a free particle. Its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wave function. The position and momentum of the particle are observables. An eigenstate of position is a wavefunction that is very large at a particular position ''x'', and zero everywhere else. If we perform a position measurement on such a wavefunction, we will obtain the result ''x'' with 100% probability. An eigenstate of momentum, on the other hand, has the form of a plane wave. It turns out that the wavelength is equal to ''h/p'', where ''h'' is Planck's constant and ''p'' is the momentum of the eigenstate. Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if we measure the observable, the wavefunction will immediately become an eigenstate of that observable. This process is known as wavefunction collapse. If we know the wavefunction at the instant before the measurement, we will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in our previous example will usually have a wavefunction that is a wave packet centered around some mean position ''x0'', neither an eigenstate of position nor of momentum. When we measure the position of the particle, it is impossible for us to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near ''x0'', where the amplitude of the wavefunction is large. After we perform the measurement, obtaining some result ''x'', the wavefunction collapses into a position eigenstate centered at ''x''. Wave functions can change as time progresses. An equation known as the Schrödinger equation describes how wave functions change in time, a role similar to Newton's second law in classical mechanics. The Schrödinger equation, applied to our free particle, predicts that the center of a wave packet will move through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain. This also has the effect of turning position eigenstates into broadened wave packets that are not position eigenstates. Some wave functions produce probability distributions that are constant in time. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherical coordinate system probability cloud surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum states, labelled ''s'', are spherically symmetric). The time evolution of wave functions is determinism in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a quantum measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e. random. The probability nature of quantum mechanics thus stems from the act of measurement: the object interacts with an apparatus, and their respective wavefunctions become entangled. In effect, the object ceases to exist as an independent entity. This may introduce some uncertainty into the prediction of what the outcome of a measurement may become, at some stage in the future, insofar as this prediction is required to draw information only from the object wavefunction. However, it might be thought that, by preparing the apparatus beforehand, its influence during the measurement might be predictable, or at least afterwards detectable, so that this kind of uncertainty might be merely a matter of insufficient data. But, as it turns out, to actually detect such influence data, by handling the apparatus, is incompatible with its functioning as a measurement device. That is, for practical reasons, the apparatus cannot do both at the same time. It is therefore a matter of principle, rather than practice, that one has the uncertainty which necessitates a probabilistic prediction. This is one of the most difficult ideas to understand about the nature of quantum systems. It was the central topic in the famous Bohr-Einstein debates, in which they sought to clarify these fundamental principles by way of thought experiments. There are some Interpretation_of_quantum_mechanics of quantum mechanics that do away with the concept of "wavefunction collapse" by altering the concept of what constitutes a "measurement" in quantum mechanics. For example, see relative state interpretation. === Quantum mechanical effects === As mentioned in the introduction, there are several classes of phenomena that appear under quantum mechanics which have no analogue in classical physics. These are sometimes referred to as "quantum effects". The first type of quantum effect is the quantization (physics) of certain physical quantities. In the example we have given, of a free particle in empty space, both the position and the momentum are continuous observables. However, if we restrict the particle to a region of space (the so-called "particle in a box" problem), the momentum observable will become discrete; it will only take on the values ''h/L'', where ''L'' is the length of the box. Such observables are said to be Quantization (physics), and they play an important role in many physical systems. Examples of quantized observables include angular momentum, the total energy of a bound system, and the energy contained in an electromagnetic wave of a given frequency. Another quantum effect is the uncertainty principle, which is the phenomenon that consecutive measurements of two or more observables may possess a fundamental limitation on accuracy. In our free particle example, it turns out that it is impossible to find a wavefunction that is an eigenstate of both position and momentum. This implies that position and momentum can never be simultaneously measured with arbitrary precision, even in principle: as the precision of the position measurement improves, the maximum precision of the momentum measurement decreases, and vice versa. Those variables for which it holds (e.g. momentum and position, or energy and time) are Hamiltonian mechanics in classical physics. Another quantum effect is the wave-particle duality. It has been shown that, under certain experimental conditions, microscopic objects like atoms or electrons exhibit particle-like behavior, such as scattering. ("Particle-like" in the sense of an object that can be localized to a particular region of space.) Under other conditions, the same type of objects exhibit wave behavior, such as Wave interference. We can observe only one type of property at a time. Another quantum effect is quantum entanglement. In some cases, the wave function of a system composed of many particles cannot be separated into independent wave functions, one for each particle. In that case, the particles are said to be "entangled". If quantum mechanics is correct, entangled particles can display remarkable and counter-intuitive properties. For example, a measurement made on one particle can produce, through the collapse of the total wavefunction, an instantaneous effect on other particles with which it is entangled, even if they are far apart. This only appears to conflict with special relativity. There is no transmission of information in the process, which would require a physical object to move (instantaneously) between the two particles. It is only by coming together, at some later meeting, that the two investigators can compare their data, and detect the remarkable correlations they contain. === Mathematical formulation === ''Main article: Mathematical formulation of quantum mechanics. See also the discussion in Quantum logic.'' In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex number Separable space Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system.) The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single electron is just the product of two complex planes. Each observable is represented by a densely-defined Hermitian (or self-adjoint operator) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues. The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (quantum mechanics), the Operator (physics) corresponding to the total energy of the system, generates time evolution. The inner product between two state vectors is a complex number known as a probability amplitude. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of ''Hermitian'' operators, for which all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing the spectral theorem of the corresponding operator. Heisenberg's uncertainty principle is represented by the statement that the operators corresponding to certain observables do not Commutator. The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the wave-like behavior of quantum states. It turns out that analytic solutions of Schrödinger's equation are only available for a small number of model Hamiltonians, of which the quantum harmonic oscillator and the hydrogen atom are the most important representatives. Even the helium atom, which contains just one more electron than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory (quantum mechanics) one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak potential energy. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of quantum chaos. An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics. ===Interactions with other scientific theories=== The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical physics when a system becomes large. This "large system" limit is known as the ''classical'' or ''correspondence limit''. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit. When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was theory of relativity classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the harmonic oscillator. Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field rather than a fixed set of particles. The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetism. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed since the inception of quantum mechanics, is to treat electric charge particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical ''1/r'' Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles. Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the subnuclear particles: quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory known as electroweak force. It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity. ==Applications of quantum theory== Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behavior of the microscopic particles that make up all forms of matter - electrons, protons, neutrons, and so forth - can often only be satisfactorily described using quantum mechanics. Quantum mechanics is important for understanding how individual atoms combine to form chemicals. The application of quantum mechanics to chemistry is known as quantum chemistry. Quantum mechanics can provide quantitative insight into chemical bonding processes by explicitly showing which molecules are energetically favorable to which others, and by approximately how much. Most of the calculations performed in computational chemistry rely on quantum mechanics. Much of modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and Magnetic Resonance Imaging. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics. Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum states over arbitrary distances. == Philosophical consequences == Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophy debate and many interpretations of quantum mechanics. Even fundamental issues such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated. The Copenhagen interpretation, due largely to Niels Bohr, was the standard interpretation of quantum mechanics when it was first formulated. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and do not simply reflect our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than Determinism. Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. He held that there should be a local hidden variable theory underlying quantum mechanics and consequently the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the EPR paradox. John Stewart Bell showed that the EPR paradox led to experimentally testable differences between quantum mechanics and local hidden variable theories. Experiments have been taken as confirming that quantum mechanics is correct and the real world cannot be described in terms of such hidden variables. "Bell test loopholes" in the experiments, however, mean the question is still not quite settled. See the Bohr-Einstein debates The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a "multiverse" composed of mostly independent parallel universes. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities because we can observe only the universe we inhabit. The Bohm interpretation, formulated by David Bohm, postulates the existence of a non-local, universal wavefunction (Schrödinger equation) which allows distant particles to interact instantaneously. Based on this interpretation, Bohm has speculated that the ultimate nature of physical reality is not a collection of separate objects (as it appears to us), but rather an undivided whole that is in perpetual dynamic flux. However, the Bohm interpretation is not popular among physicists, largely because it is considered very inelegant. == History == In 1900, Max Planck introduced the idea that energy is quantized, in order to derive a formula for the observed frequency dependence of the energy emitted by a black body. In 1905, Einstein explained the photoelectric effect by postulating that light energy comes in quanta called photons. In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization. In 1924, Louis-Victor de Broglie put forward his theory of matter waves. These theories, though successful, were strictly phenomenology (science): there was no rigorous justification for quantization. They are collectively known as the ''old quantum theory''. The phrase "quantum physics" was first used in Johnston's ''Planck's Universe in Light of Modern Physics''. Modern quantum mechanics was born in 1925, when Werner Heisenberg developed matrix mechanics and Erwin Schrödinger invented wave mechanics and the Schrödinger equation. Schrödinger subsequently showed that the two approaches were equivalent. Heisenberg formulated his uncertainty principle in 1927, and the Copenhagen interpretation took shape at about the same time. Starting around 1927, Paul Dirac unified quantum mechanics with special relativity. He also pioneered the use of operator theory, including the influential bra-ket notation, as described in his famous 1930 textbook. During the same period, John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period still stand, and remain widely used. The field of quantum chemistry was pioneered by Walter Heitler and Fritz London, who published a study of the covalent bond of the hydrogen molecule in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American chemist Linus Pauling. Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than single particles, resulting in what are known as Quantum field theory. Early workers in this area included Paul Dirac, Wolfgang Pauli, Victor Weisskopf, and Pascaul Jordan. This area of research culminated in the formulation of quantum electrodynamics by Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro Tomonaga during the 1940s. Quantum electrodynamics is a quantum theory of electrons, positrons, and the electromagnetic field, and served as a role model for subsequent quantum field theories. The many worlds interpretation was formulated by Hugh Everett in 1956. The theory of quantum chromodynamics was formulated beginning in the early 1960s. The theory as we know it today was formulated by Politzer, Gross and Wilzcek in 1975. Building on pioneering work by Schwinger, Peter Higgs, Goldstone and others, Sheldon Lee Glashow, Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. ===Founding experiments=== * Thomas Young (scientist)'s double-slit experiment proving the wave nature of light (c1805) * Henri Becquerel discovers radioactivity (1896) * Joseph John Thomson's cathode ray tube experiments (discovers the electron and its negative charge) (1897) * The study of black body radiation between 1850 and 1900, which could not be explained without quantum concepts. * The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy * Robert Millikan's oil-drop experiment, which showed that electric charge occurs as ''quantum'' (whole units), (1909) * Ernest Rutherford's gold foil experiment disproved the plum pudding model of the atom which suggested that the positive charge and mass of the atom are almost uniformly distributed. (1911) * Otto Stern and Walter Gerlach conduct the Stern-Gerlach experiment, which demonstrates the quantized nature of particle Spin (physics) (1920) * Clinton Davisson and Lester Germer demonstrate the wave nature of the electron (1927) *Clyde L. Cowan and Frederick Reines confirm the existence of the neutrino in the neutrino experiment (1955) == See also == * Quantum electrochemistry * Quantum information * Measurement in quantum mechanics == References == * Mackey, George Whitelaw (2004). ''The mathematical foundations of quantum mechanics''. Dover Publications. ISBN 0486435172. ==Notes== *[http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html The Davisson-Germer experiment, which demonstrates the wave nature of the electron] == External links == *[http://plato.stanford.edu/entries/qm Quantum Mechanics (''Stanford Encyclopedia of Philosophy'')] *[http://www.mtnmath.com/faq/meas-qm.html Quantum mechanics] *[http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics] *[http://www.physicstoday.org/pt/vol-54/iss-2/p11.html David Mermin on the future directions of physics] *[http://www.decoherence.de New developments in the understanding of the quantum-classical relation] *[http://higgo.com/quantum/laymans.htm A Lazy Layman's Guide to Quantum Physics] *[http://www.thch.uni-bonn.de/tc/people/brems.vincent/vincent/faq.html A short FAQ on quantum resonances] Quantum mechanics lv:Kvantu mehānika vi:Cơ học lượng tử
Quantum mechanics
---- Discussion archives: /Archive1 – /Archive2 (2004) ---- ==Experimental confirmation of predictions== As it stands, experimental confirmation of the theory seems to be mentioned only within the "philosophical consequences" section, where it crops up in relation to the Bell tests and entanglement. Perhaps "Experimental confirmation" should be a section of its own? User:Caroline Thompson 17:14, 14 Jan 2005 (UTC) :I suggest a separate article; otherwise , too much in one article. ==wording quibble== "Quantum mechanics is a physical theory which, for very small objects such as atoms, produces results that are very different and much more accurate than those of classical mechanic" First, it's not just small things, there are macroscopic q. phenomena, eg superconductivity/fluidity/lasers blackbody radiation spectra, heat content of solids, etc ; and it's not that for atoms it provides a more accurate theroy than classical mech, it's that classical mech. doesn't provide ANY theory that's EVEN CLOSE to the facts, for atoms, and those other things I just mentioned. Needs rewriting.User:67.118.116.145 04:38, 21 Jan 2005 (UTC) :I agree with your points. I made an attempt to address them. Tell me what you think. -User:Lethe | User talk:Lethe 05:14, Jan 21, 2005 (UTC) == Gnome!? == In a recent edit, someone added a picture of a garden gnome and nothing else. I could just be missing some obvious connection between gnomes and quantum mechanics, but I doubt it. I'm removing it for the moment. ==Feynman== Richard Feynman was not among the founding fathers of QM. I added Pauli's name there instead.--User:Ashujo Feb 11, 2005 == More founding experiments? == Doesn't the line spectra of atomic hydrogen hold its place among the ones mentioned? I am from Sweden so I might be biase to Rydberg, but I guess Bohr migh side with me on this... Maybe also the photo-ekectric effect - connecting Plank's constant with something else than the black-bodies? == more fundamental theory == User:CYD, I noticed that you removed my remark about quantum mechanics being suitable a more fundamental theory. Didn't you like it? Basically, I have in mind that any theory with the larger domain of applicability should be said to be more fundamental. -User:Lethe | User talk:Lethe 08:00, Mar 3, 2005 (UTC) :Okay, now I see what you are getting at. I put it back in a slightly different form. -- User:CYD == new intro == I have some comments about the new intro: # I like the idea of the new intro. It would be useful to put quantum mechanics into the larger context of other kinds of mechanics. # but don't just insert a new intro in front of the existing intro # respect the conventions of the article. For example, this article uses the phrase "quantum mechanics" to mean any theory that is quantized. Therefore, to distinguish quantum mechanics from relativistic quantum mechanics is confusing. # furthermore, I would not seperate relativistic quantum mechanics from nonrelativistic quantum mechanics. The only difference between the two is basically a choice of Hamiltonian. # quantum field theory, on the other hand, is the true marriage of quantum mechanics and relativity. And it is a qualitatively different theory from quantum mechanics (single particle). # what you consider to be a significant fraction of the speed of light depends of course on your needs. GPS satellites probably don't even go 0.1% the speed of light, but still the engineers use relativistic mechanics with them. Because they require great accuracy. # we changed in the old intro some wording to make clear that it's not the smallness that makes quantum mechanics apply. Some atoms are classical, and some macroscopic systems are quantum. So it's inaccurate to just say "small things like atoms" are quantum systems. and again, it depends on the level of accuracy. #Classical mechanics includes many things besides Newtonian mechanics. I would distinguish Hamiltonian and Lagrangian mechanics from Newtonian mechanics. I might also distinguish fluid mechanics, statistical mechanics. # what about general relativity? Shouldn't it fit in some where? -User:Lethe | User talk:Lethe 23:40, Apr 13, 2005 (UTC) : :To make the article less tedious, how about moving the first five paragraphs elsewhere to other articles in the physics category? This preliminary non-quantum prose might even be a welcome addition to a section of the major physics article. The state of the article when it had just become featured was pretty good. Right now, a re-run of other topics makes for tedious reading. There isn't an equation in sight, for some reason. User:Ancheta Wis 00:38, 14 Apr 2005 (UTC) My thanks to LauraScudder for the improvements as I was typing this. :As of 08:36, 14 Apr 2005 (UTC), the first paragraph belongs to a parent article. My vote is to move it to physics or mechanics. User:Ancheta Wis 08:36, 14 Apr 2005 (UTC) :The new intro has got us arguing over whether Newtonian mechanics is all there is to classical mechanics and I've been editing such things too until I realized that the subfields of classical mechanics have nothing to do with quantum mechanics and just distract and confuse the unintiated while boring the others. I shortened that segment to: ::''Most physicists would divide mechanics into four major areas: classical mechanics, Theory of relativity mechanics, and quantum mechanics. ::But in physics, quantum mechanics can be regarded as ''the'' fundamental theory. '' :I think it simplifies the intro significantly and takes it back to the spirit of the first featured version while still putting the field into context for those who want to clicky clicky like mad. The distinction between nonrelativistic quantum mechanics and relativistic quantum field theory is made on the appropriate quantum field theory pages.--User:Laurascudder 18:28, 14 Apr 2005 (UTC) == Introduction == You are losing our reader with this introduction, although the worst was taken care of during the last few days. Please consider the frame-of-mind of someone seeking info on "quantum mechanics" as a fairly unfamiliar topic. This reader does not want to hear about Newtonian mechanics, or relativity, or any number of other fancy classifications, at least not until later. Give the reader a break, at plainly start by telling what it is about. And why anyone should take an interest, besides the specialists. April 15, 2005 - Guest :I agree, in making the introduction more "accessible", we have severely bogged it down. Also doesn't really match the Wikipedia:WikiProject Science guidelines now either. I'll be bold and if people disagree, edit away and/or discuss here. --User:Laurascudder 18:13, 14 Apr 2005 (UTC) ::Yes, much nicer. However, I have to say that "relativistic" should not be extracted from either classical or quantum mechanics. Both include relativity (special, of course), and one takes a non-relativistic limit as the need arises. I know that most university course plans start out non-relativistically, and this should of course be mentioned, and is quite reasonable, but it is not really fundamental. We don't hit students with relativity on day one, of course (we wait a couple of months:-). Also, something must be done for the general readers, there has got to be many at this place, and they should be able to come away with something too. -Guest April 15, 2005 It appears you are advocating the position of a reader who has not yet considered the microcosm. This suggests that the article might start off with the atomic hypothesis, then radioactive decay, or perhaps cosmic rays (leakage from a Leyden jar, etc.). ... This approach might then culminate with the statement about general applicability of QM as a fundamental theory, and the current non-relationship to GR. A complete rewrite or new article history of quantum mechanics. User:Ancheta Wis 10:32, 15 Apr 2005 (UTC) ( By the way, you can date-time-stamp your posts with the 5-tilde notation:
Quantum mechanics
Quantum mechanics (also called quantum physics or quantum theory) is a physics theory that is believed to be the formalism underlying the description of all physical systems. Quantum mechanical departures from classical physics are most often encountered at small length scales, low energies and/or low temperatures. Physics Mechanics Physical chemistry vi:Category:Cơ học lượng tử
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