   #copyright

Quantum mechanics

2007 Schools Wikipedia Selection. Related subjects: General Physics

   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. Wavefunctions like
   these are directly comparable to Chladni's figures of acoustic modes of
   vibration in classical physics and are indeed modes of oscillation as
   well: they possess a sharp energy and thus a sharp frequency. The
   angular momentum and energy are quantized, and only take on discrete
   values like those shown (as is the case for resonant frequencies in
   acoustics).
   Enlarge
   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. Wavefunctions like
   these are directly comparable to Chladni's figures of acoustic modes of
   vibration in classical physics and are indeed modes of oscillation as
   well: they possess a sharp energy and thus a sharp frequency. The
   angular momentum and energy are quantized, and only take on discrete
   values like those shown (as is the case for resonant frequencies in
   acoustics).

   Quantum mechanics is a fundamental branch of theoretical physics that
   replaces classical mechanics and classical electromagnetism at the
   atomic and subatomic levels. It is the underlying mathematical
   framework of many fields of physics and chemistry, including condensed
   matter physics, atomic physics, molecular physics, computational
   chemistry, quantum chemistry, particle physics, and nuclear physics.
   Along with general relativity, quantum mechanics is one of the pillars
   of modern physics.

Introduction

   The term quantum (Latin, "how much") refers to discrete units that the
   theory assigns to certain physical quantities, such as the energy of an
   atom at rest (see Figure 1, at right). The discovery that waves could
   be measured in particle-like small packets of energy called quanta led
   to the branch of physics that deals with atomic and subatomic systems
   which we today call Quantum Mechanics. The foundations of quantum
   mechanics were established during the first half of the twentieth
   century by Werner Heisenberg, Max Planck, Louis de Broglie, Niels Bohr,
   Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Albert
   Einstein, Wolfgang Pauli and others. Some fundamental aspects of the
   theory are still actively studied.

   Quantum mechanics is a more fundamental theory than Newtonian mechanics
   and classical electromagnetism, in the sense that it provides accurate
   and precise descriptions for many phenomena that these "classical"
   theories simply cannot explain on the atomic and subatomic level. It is
   necessary to use quantum mechanics to understand the behaviour of
   systems at atomic length scales and smaller. For example, if Newtonian
   mechanics governed the workings of an atom, electrons would rapidly
   travel towards and collide with the nucleus. However, in the natural
   world the electron normally remains in a stable orbit around a nucleus
   — seemingly defying classical electromagnetism.

   Quantum mechanics was initially developed to explain the atom,
   especially the spectra of light emitted by different atomic species.
   The quantum theory of the atom developed as an explanation for the
   electron's staying in its orbital, which could not be explained by
   Newton's laws of motion and by classical electromagnetism.

   In the formalism of quantum mechanics, the state of a system at a given
   time is described by a complex wave function (sometimes referred to as
   orbitals in the case of atomic electrons), and more generally, elements
   of a complex vector space. This abstract mathematical object allows for
   the calculation of probabilities of outcomes of concrete experiments.
   For example, it allows one to compute the probability of finding an
   electron in a particular region around the nucleus at a particular
   time. Contrary to classical mechanics, one cannot ever make
   simultaneous predictions of conjugate variables, such as position and
   momentum, with arbitrary accuracy. For instance, electrons may be
   considered to be located somewhere within a region of space, but with
   their exact positions being unknown. Contours of constant probability,
   often referred to as “clouds” may be drawn around the nucleus of an
   atom to conceptualise where the electron might be located with the most
   probability. It should be stressed that the electron itself is not
   spread out over such cloud regions. It is either in a particular region
   of space, or it is not. Heisenberg's uncertainty principle quantifies
   the inability to precisely locate the particle.

   The other exemplar that led to quantum mechanics was the study of
   electromagnetic waves such as light. When it was found in 1900 by Max
   Planck that the energy of waves could be described as consisting of
   small packets or quanta, Albert Einstein exploited this idea to show
   that an electromagnetic wave such as light could be described by a
   particle called the photon with a discrete energy dependent on its
   frequency. This led to a theory of unity between subatomic particles
   and electromagnetic waves called wave-particle duality in which
   particles and waves were neither one nor the other, but had certain
   properties of both. While quantum mechanics describes the world of the
   very small, it also is needed to explain certain " macroscopic quantum
   systems" such as superconductors and superfluids.

   Broadly speaking, quantum mechanics incorporates four classes of
   phenomena that classical physics cannot account for: (i) the
   quantization (discretization) of certain physical quantities, (ii)
   wave-particle duality, (iii) the uncertainty principle, and (iv)
   quantum entanglement. Each of these phenomena will be described in
   greater detail in subsequent sections.

   Since the early days of quantum theory, physicists have made many
   attempts to combine it with the other highly successful theory of the
   twentieth century, Albert Einstein's General Theory of Relativity.
   While quantum mechanics is entirely consistent with special relativity,
   serious problems emerge when one tries to join the quantum laws with
   general relativity, a more elaborate description of spacetime which
   incorporates gravitation. Resolving these inconsistencies has been a
   major goal of twentieth- and twenty-first-century physics. Despite the
   proposal of many novel ideas, the unification of quantum
   mechanics—which reigns in the domain of the very small—and general
   relativity—a superb description of the very large—remains a tantalizing
   future possibility. (See quantum gravity, string theory.)

   Because everything is composed of quantum-mechanical particles, the
   laws of classical physics must approximate the laws of quantum
   mechanics in the appropriate limit. This is often expressed by saying
   that in case of large quantum numbers quantum mechanics "reduces" to
   classical mechanics and classical electromagnetism. This requirement is
   called the correspondence, or classical limit.

Theory

   There are numerous mathematically equivalent formulations of quantum
   mechanics. One of the oldest and most commonly used formulations is the
   transformation theory invented by Cambridge theoretical physicist 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 instantaneous state of a quantum system
   encodes the probabilities of its measurable properties, or "
   observables". Examples of observables include energy, position,
   momentum, and angular momentum. Observables can be either continuous
   (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). In
   the everyday world, it is natural and intuitive to think of everything
   being in an eigenstate of every observable. Everything appears to have
   a definite position, a definite momentum, and a definite time of
   occurrence. However, quantum mechanics does not pinpoint the exact
   values for the position or momentum of a certain particle in a given
   space in a finite time, but, rather, it only provides a range of
   probabilities of where that particle might be. Therefore, it became
   necessary to use different words for a) the state of something having
   an uncertainty relation and b) a state that has a definite value. The
   latter is called the "eigenstate" of the property being measured.

   A concrete example will be useful here. Let us consider a free
   particle. In quantum mechanics, there is wave-particle duality so the
   properties of the particle can be described as a wave. Therefore, its
   quantum state can be represented as a wave, of arbitrary shape and
   extending over all of space, called a wavefunction. The position and
   momentum of the particle are observables. The Uncertainty Principle of
   quantum mechanics states that both the position and the momentum cannot
   simultaneously be known with infinite precision at the same time.
   However, we can measure just the position alone of a moving free
   particle creating an eigenstate of position with 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. In other words, we will know the
   position of the free particle. This is called an eigenstate of
   position. If the particle is in an eigenstate of position then its
   momentum is completely unknown. An eigenstate of momentum, on the other
   hand, has the form of a plane wave. It can be shown that the wavelength
   is equal to h/p, where h is Planck's constant and p is the momentum of
   the eigenstate. If the particle is in an eigenstate of momentum then
   its position is completely blurred out.

   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 instantaneously be an eigenstate of that observable.
   This process is known as wavefunction collapse. It involves expanding
   the system under study to include the measurement device, so that a
   detailed quantum calculation would no longer be feasible and a
   classical description must be used. 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
   x[0], 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 x[0], 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
   centre 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 (which can be thought of as infinitely
   sharp wave packets) into broadened wave packets that are no longer
   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, spherically
   symmetric wavefunction surrounding the nucleus (Fig. 1). (Note that
   only the lowest angular momentum states, labeled s, are spherically
   symmetric).

   The time evolution of wave functions is deterministic 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
   measurement, the change of the wavefunction into another one is not
   deterministic, but rather unpredictable, i.e., random.

   The probabilistic nature of quantum mechanics thus stems from the act
   of measurement. This is one of the most difficult aspects of quantum
   systems to understand. It was the central topic in the famous
   Bohr-Einstein debates, in which the two scientists attempted to clarify
   these fundamental principles by way of thought experiments. In the
   decades after the formulation of quantum mechanics, the question of
   what constitutes a "measurement" has been extensively studied.
   Interpretations of quantum mechanics have been formulated to do away
   with the concept of "wavefunction collapse"; see, for example, the
   relative state interpretation. The basic idea is that when a quantum
   system interacts with a measuring apparatus, their respective
   wavefunctions become entangled, so that the original quantum system
   ceases to exist as an independent entity. For details, see the article
   on measurement in quantum mechanics.

Mathematical formulation

   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 separable Hilbert space
   (variously called the "state space" or the "associated Hilbert space"
   of the system) well defined up to a complex number of norm 1 (the phase
   factor). In other words, the possible states are points in the
   projectivization of a Hilbert space. 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 proton is
   just the product of two complex planes. Each observable is represented
   by a densely defined Hermitian (or self-adjoint) 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, the operator 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 decomposition of
   the corresponding operator. Heisenberg's uncertainty principle is
   represented by the statement that the operators corresponding to
   certain observables do not commute.

   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 behaviour 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, the particle in a box, the
   hydrogen-molecular ion 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 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 behaviour. 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 moves to higher
   energies or equivalently, larger quantum numbers. This "high energy"
   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.
   Unsolved problems in physics: In the correspondence limit of quantum
   mechanics: Is there a preferred interpretation of quantum mechanics?
   How does the quantum description of reality, which includes elements
   such as the superposition of states and wavefunction collapse, give
   rise to the reality we perceive?

   When quantum mechanics was originally formulated, it was applied to
   models whose correspondence limit was non-relativistic 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
   classical 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
   electromagnetic interaction.

   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 charged 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 -\frac{e^2}{4 \pi\ \epsilon_0\ } \frac{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 theory.

   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

   Quantum mechanics has had enormous success in explaining many of the
   features of our world. The individual behaviour of the subatomic
   particles that make up all forms of matter - electrons, protons,
   neutrons, photons and so forth - can often only be satisfactorily
   described using quantum mechanics. Quantum mechanics has strongly
   influenced string theory, a candidate for a theory of everything (see
   Reductionism). It is also related to statistical mechanics.

   Quantum mechanics is important for understanding how individual atoms
   combine covalently to form chemicals or molecules. The application of
   quantum mechanics to chemistry is known as quantum chemistry.
   (Relativistic) quantum mechanics can in principle mathematically
   describe most of chemistry. Quantum mechanics can provide quantitative
   insight into ionic and covalent 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 philosophical debate and many
   interpretations. 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 the Danish theoretical
   physicist Niels Bohr, is the interpretation of quantum mechanics most
   widely accepted amongst physicists. According to it, the probabilistic
   nature of quantum mechanics predictions cannot be explained in terms of
   some other deterministic theory, and does not simply reflect our
   limited knowledge. Quantum mechanics provides probabilistic results
   because the physical universe is itself probabilistic rather than
   deterministic.

   Albert Einstein, himself one of the founders of quantum theory,
   disliked this loss of determinism in measurement (Hence his famous
   quote "God does not play dice with the universe."). 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 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. " Potential loopholes" in
   the experiments, however, mean that the question is still not quite
   settled.

   The writer C.S. Lewis viewed QM as incomplete, because notions of
   indeterminism did not agree with his religious beliefs. Lewis, a
   professor of English, was of the opinion that the Heisenberg
   uncertainty principle was more of an epistemic limitation than an
   indication of ontological indeterminacy, and in this respect believed
   similarly to many advocates of hidden variables theories. The
   Bohr-Einstein debates provide a vibrant critique of the Copenhagen
   Interpretation from an epistemological point of view.

   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.
   This is not accomplished by introducing some new axiom to quantum
   mechanics, but on the contrary by removing the axiom of the collapse of
   the wave packet: All the possible consistent states of the measured
   system and the measuring apparatus (including the observer) are present
   in a real physical (not just formally mathematical, as in other
   interpretations) quantum superposition. (Such a superposition of
   consistent state combinations of different systems is called an
   entangled state.) While the multiverse is deterministic, we perceive
   non-deterministic behaviour governed by probabilities, because we can
   observe only the universe, i.e. the consistent state contribution to
   the mentioned superposition, we inhabit. Everett's interpretation is
   perfectly consistent with John Bell's experiments and makes them
   intuitively understandable. However, according to the theory of quantum
   decoherence, the parallel universes will never be accessible for us,
   making them physically meaningless. This inaccessiblity can be
   understood as follows: once a measurement is done, the measured system
   becomes entangled with both the physicist who measured it and a huge
   number of other particles, some of which are photons flying away
   towards the other end of the universe; in order to prove that the wave
   function did not collapse one would have to bring all these particles
   back and measure them again, together with the system that was measured
   originally. This is completely impractical, but even if one can
   theoretically do this, it would destroy any evidence that the original
   measurement took place (including the physicist's memory).

History

   In 1900, the German physicist 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. The idea that each photon had to
   consist of energy in terms of quanta was a remarkable achievement as it
   effectively removed the possibility of black body radiation attaining
   infinite energy if it were to be explained in terms of wave forms only.
   In 1913, Bohr explained the spectral lines of the hydrogen atom, again
   by using quantization, in his paper of July 1913 On the Constitution of
   Atoms and Molecules. In 1924, the French physicist Louis de Broglie put
   forward his theory of matter waves by stating that particles can
   exhibit wave characteristics and vice versa.

   These theories, though successful, were strictly phenomenological:
   there was no rigorous justification for quantization (aside, perhaps,
   for Henri Poincaré's discussion of Planck's theory in his 1912 paper
   Sur la théorie des quanta). 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 the German physicist
   Heisenberg developed matrix mechanics and the Austrian physicist
   Schrödinger invented wave mechanics and the non-relativistic
   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 began the process of unifying quantum mechanics
   with special relativity by proposing the Dirac equation for the
   electron. 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, Hungarian polymath 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 physicists 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
   theoretical chemist Linus Pauling at Cal Tech, and John Slater into
   various theories such as Molecular Orbital Theory or Valence Theory.

   Beginning in 1927, attempts were made to apply quantum mechanics to
   fields rather than single particles, resulting in what are known as
   quantum field theories. Early workers in this area included Dirac,
   Pauli, Weisskopf, and Jordan. This area of research culminated in the
   formulation of quantum electrodynamics by Feynman, Dyson, Schwinger,
   and 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 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,
   Higgs, Goldstone, Glashow, Weinberg and Salam independently showed how
   the weak nuclear force and quantum electrodynamics could be merged into
   a single electroweak force.

Founding experiments

     * Thomas Young's double-slit experiment demonstrating 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 quanta (whole units), (1909)
     * Ernest Rutherford's gold foil experiment disproved the plum pudding
       model of the atom which suggested that the mass and positive charge
       of the atom are almost uniformly distributed. (1911)
     * Otto Stern and Walther Gerlach conduct the Stern-Gerlach
       experiment, which demonstrates the quantized nature of particle
       spin (1920)
     * Clinton Davisson and Lester Germer demonstrate the wave nature of
       the electron in the Electron diffraction experiment (1927)
     * Clyde L. Cowan and Frederick Reines confirm the existence of the
       neutrino in the neutrino experiment (1955)
     * Claus Jönsson`s double-slit experiment with electrons (1961)
     * The Quantum Hall effect, discovered in 1980 by Klaus von Klitzing.
       The quantized version of the Hall effect has allowed for the
       definition of a new practical standard for electrical resistance
       and for an extremely precise independent determination of the fine
       structure constant.

Footnote

    1. ^ Especially since Werner Heisenberg was awarded the Nobel Prize in
       Physics in 1932 for the creation of quantum mechanics, the role of
       Max Born has been obfuscated. A 2005 biography of Born details his
       role as the creator of the matrix formulation of quantum mechanics.
       This was recognized in a paper by Heisenberg, in 1950, honoring Max
       Planck. See: Nancy Thorndike Greenspan, “The End of the Certain
       World: The Life and Science of Max Born (Basic Books, 2005), pp.
       124 - 128, and 285 - 286.
    2. ^
    3. ^ The Davisson-Germer experiment, which demonstrates the wave
       nature of the electron

   Retrieved from " http://en.wikipedia.org/wiki/Quantum_mechanics"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
