# quantum theory

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## quantum theory,

modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity**relativity,**

physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.

**.....**Click the link for more information. together form the theoretical basis of modern physics. Just as the theory of relativity assumes importance in the special situation where very large speeds are involved, so the quantum theory is necessary for the special situation where very small quantities are involved, i.e., on the scale of molecules

**molecule**

[New Lat.,=little mass], smallest particle of a compound that has all the chemical properties of that compound. A single atom is usually not referred to as a molecule, and ionic compounds such as common salt are not made up of molecules.

**.....**Click the link for more information. , atoms

**atom**

[Gr.,=uncuttable (indivisible)], basic unit of matter; more properly, the smallest unit of a chemical element having the properties of that element.

**Structure of the Atom**

**.....**Click the link for more information. , and elementary particles

**elementary particles,**

the most basic physical constituents of the universe.

**Basic Constituents of Matter**

Molecules are built up from the atom, which is the basic unit of any chemical element. The atom in turn is made from the proton, neutron, and electron.

**.....**Click the link for more information. . Aspects of the quantum theory have provoked vigorous philosophical debates concerning, for example, the uncertainty principle and the statistical nature of all the predictions of the theory.

### Relationship of Energy and Matter

According to the older theories of classical physics, energy is treated solely as a continuous phenomenon, while matter is assumed to occupy a very specific region of space and to move in a continuous manner. According to the quantum theory, energy is held to be emitted and absorbed in tiny, discrete amounts. An individual bundle or packet of energy, called a quantum (pl. quanta), thus behaves in some situations much like particles of matter; particles are found to exhibit certain wavelike properties when in motion and are no longer viewed as localized in a given region but rather as spread out to some degree.

For example, the light or other radiation given off or absorbed by an atom has only certain frequencies (or wavelengths), as can be seen from the line spectrum**spectrum,**

arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph).**.....** Click the link for more information. associated with the chemical element represented by that atom. The quantum theory shows that those frequencies correspond to definite energies of the light quanta, or photons**photon**

, the particle composing light and other forms of electromagnetic radiation, sometimes called light quantum. The photon has no charge and no mass. About the beginning of the 20th cent.**.....** Click the link for more information. , and result from the fact that the electrons of the atom can have only certain allowed energy values, or levels; when an electron changes from one allowed level to another, a quantum of energy is emitted or absorbed whose frequency is directly proportional to the energy difference between the two levels.

### Dual Nature of Waves and Particles

The restriction of the energy levels of the electrons is explained in terms of the wavelike properties of their motions: electrons occupy only those orbits for which their associated wave is a standing wave (i.e., the circumference of the orbit is exactly equal to a whole number of wavelengths) and thus can have only those energies that correspond to such orbits. Moreover, the electrons are no longer thought of as being at a particular point in the orbit but rather as being spread out over the entire orbit. Just as the results of relativity approximate those of Newtonian physics when ordinary speeds are involved, the results of the quantum theory agree with those of classical physics when very large "quantum numbers" are involved, i.e., on the ordinary large scale of events; this agreement in the classical limit is required by the correspondence principle**correspondence principle,**

physical principle, enunciated by Niels Bohr in 1923, according to which the predictions of the quantum theory must correspond to the predictions of the classical theories of physics when the quantum theory is used to describe the behavior of systems**.....** Click the link for more information. of Niels Bohr**Bohr, Niels Henrik David**

, 1885–1962, Danish physicist, one of the foremost scientists of modern physics. He studied at the Univ. of Copenhagen (Ph.D. 1911) and carried on research on the structure of the atom at Cambridge under Sir James J.**.....** Click the link for more information. . The quantum theory thus proposes a dual nature for both waves and particles, one aspect predominating in some situations, the other predominating in other situations.

### Evolution of Quantum Theory

#### Early Developments

While the theory of relativity was largely the work of one man, Albert Einstein**Einstein, Albert**

, 1879–1955, American theoretical physicist, known for the formulation of the relativity theory, b. Ulm, Germany. He is recognized as one of the greatest physicists of all time.**.....** Click the link for more information. , the quantum theory was developed principally over a period of thirty years through the efforts of many scientists. The first contribution was the explanation of blackbody**blackbody,**

in physics, an ideal black substance that absorbs all and reflects none of the radiant energy falling on it. Lampblack, or powdered carbon, which reflects less than 2% of the radiation falling on it, crudely approximates an ideal blackbody; a material consisting of a**.....** Click the link for more information. radiation in 1900 by Max Planck**Planck, Max**

, 1858–1947, German physicist. Seeking to explain the experimental spectrum (distribution of electromagnetic energy according to wavelength) of blackbody radiation, he introduced the hypothesis (1900) that oscillating atoms absorb and emit energy only in**.....** Click the link for more information. , who proposed that the energies of any harmonic oscillator (see harmonic motion**harmonic motion,**

regular vibration in which the acceleration of the vibrating object is directly proportional to the displacement of the object from its equilibrium position but oppositely directed.**.....** Click the link for more information. ), such as the atoms of a blackbody radiator, are restricted to certain values, each of which is an integral (whole number) multiple of a basic, minimum value. The energy *E* of this basic quantum is directly proportional to the frequency ν of the oscillator, or *E*=*h*ν, where *h* is a constant, now called Planck's constant, having the value 6.62607×10^{−34} joule-second. In 1905, Einstein proposed that the radiation itself is also quantized according to this same formula, and he used the new theory to explain the photoelectric effect**photoelectric effect,**

emission of electrons by substances, especially metals, when light falls on their surfaces. The effect was discovered by H. R. Hertz in 1887. The failure of the classical theory of electromagnetic radiation to explain it helped lead to the development of**.....** Click the link for more information. . Following the discovery of the nuclear atom by Rutherford**Rutherford, Ernest Rutherford, 1st Baron,**

1871–1937, British physicist, b. New Zealand. Rutherford left New Zealand in 1895, having earned three degrees from the Univ.**.....** Click the link for more information. (1911), Bohr used the quantum theory in 1913 to explain both atomic structure and atomic spectra, showing the connection between the electrons' energy levels and the frequencies of light given off and absorbed.

#### Quantum Mechanics and Later Developments

Quantum mechanics, the final mathematical formulation of the quantum theory, was developed during the 1920s. In 1924, Louis de Broglie**Broglie, Louis Victor, duc de,**

1892–1987, French physicist. In 1928 he became professor in the faculty of sciences, Univ. of Paris. It was known from the earlier quantum theory that light waves sometimes exhibited a particlelike behavior.**.....** Click the link for more information. proposed that not only do light waves sometimes exhibit particlelike properties, as in the photoelectric effect and atomic spectra, but particles may also exhibit wavelike properties. This hypothesis was confirmed experimentally in 1927 by C. J. Davisson**Davisson, Clinton Joseph**

, 1881–1958, American physicist, b. Bloomington, Ill. He joined the engineering department of the Bell Telephone Laboratories in 1917. Davisson worked on thermionics, magnetism, and electron diffraction. His demonstrations with L. H.**.....** Click the link for more information. and L. H. Germer, who observed diffraction**diffraction,**

bending of waves around the edge of an obstacle. When light strikes an opaque body, for instance, a shadow forms on the side of the body that is shielded from the light source.**.....** Click the link for more information. of a beam of electrons analogous to the diffraction of a beam of light. Two different formulations of quantum mechanics were presented following de Broglie's suggestion. The wave mechanics of Erwin Schrödinger**Schrödinger, Erwin**

, 1887–1961, Austrian theoretical physicist. He was educated at Vienna, taught at Breslau and Zürich, and was professor at the Univ. of Berlin (1927–33), fellow of Magdalen College, Oxford (1933–36), and professor at the Univ.**.....** Click the link for more information. (1926) involves the use of a mathematical entity, the wave function, which is related to the probability of finding a particle at a given point in space. The matrix mechanics of Werner Heisenberg (1925) makes no mention of wave functions or similar concepts but was shown to be mathematically equivalent to Schrödinger's theory.

Quantum mechanics was combined with the theory of relativity in the formulation of P. A. M. Dirac**Dirac, Paul Adrien Maurice**

, 1902–84, English physicist. He was educated at the Univ. of Bristol and St. John's College, Cambridge, and became professor of mathematics at Cambridge in 1932.**.....** Click the link for more information. (1928), which, in addition, predicted the existence of antiparticles**antiparticle,**

elementary particle corresponding to an ordinary particle such as the proton, neutron, or electron, but having the opposite electrical charge and magnetic moment.**.....** Click the link for more information. . A particularly important discovery of the quantum theory is the uncertainty principle**uncertainty principle,**

physical principle, enunciated by Werner Heisenberg in 1927, that places an absolute, theoretical limit on the combined accuracy of certain pairs of simultaneous, related measurements.**.....** Click the link for more information. , enunciated by Heisenberg**Heisenberg, Werner**

, 1901–76, German physicist. One of the founders of the quantum theory, he is best known for his uncertainty principle, or indeterminacy principle, which states that it is impossible to determine with arbitrarily high accuracy both the position and**.....** Click the link for more information. in 1927, which places an absolute theoretical limit on the accuracy of certain measurements; as a result, the assumption by earlier scientists that the physical state of a system could be measured exactly and used to predict future states had to be abandoned. Other developments of the theory include quantum statistics, presented in one form by Einstein and S. N. Bose (the Bose-Einstein statistics**Bose-Einstein statistics,**

class of statistics that applies to elementary particles called bosons, which include the photon, pion, and the W and Z particles. Bosons have integral values of the quantum mechanical property called spin and are "gregarious" in the sense that an**.....** Click the link for more information. ) and in another by Dirac and Enrico Fermi**Fermi, Enrico**

, 1901–54, American physicist, b. Italy. He studied at Pisa, Göttingen, and Leiden, and taught physics at the universities of Florence and Rome. He contributed to the early theory of beta decay and the neutrino and to quantum statistics.**.....** Click the link for more information. (the Fermi-Dirac statistics**Fermi-Dirac statistics,**

class of statistics that applies to particles called fermions. Fermions have half-integral values of the quantum mechanical property called spin and are "antisocial" in the sense that two fermions cannot exist in the same state.**.....** Click the link for more information. ); quantum electrodynamics**quantum electrodynamics**

(QED), quantum field theory that describes the properties of electromagnetic radiation and its interaction with electrically charged matter in the framework of quantum theory.**.....** Click the link for more information. , concerned with interactions between charged particles and electromagnetic fields**field,**

in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. The field concept was developed by M.**.....** Click the link for more information. ; its generalization, quantum field theory**quantum field theory,**

study of the quantum mechanical interaction of elementary particles and fields. Quantum field theory applied to the understanding of electromagnetism is called quantum electrodynamics (QED), and it has proved spectacularly successful in describing the**.....** Click the link for more information. ; and quantum electronics.

### Bibliography

See W. Heisenberg, *The Physical Principles of the Quantum Theory* (1930) and *Physics and Philosophy* (1958); G. Gamow, *Thirty Years that Shook Physics* (1966); J. Gribbin, *In Search of Schrödinger's Cat* (1984).

## quantum theory

The theory put forward by the German physicist Max Planck in 1900. Classical physics regarded all changes in the physical properties of a system to be continuous. By departing from this viewpoint and allowing physical quantities such as energy, angular momentum, and action to change only by discrete amounts, quantum theory was born. It grew out of Planck's attempts to explain the form of the curves of intensity against wavelength for a black-body radiator. By assuming that energy could only be emitted and absorbed in discrete amounts, called quanta, he was successful in describing the shape of the curves. Other early applications of quantum theory were Einstein's explanation of the photoelectric effect and Bohr's theory of the atom (see hydrogen spectrum; energy level). The more precise mathematical theory that developed in the 1920s from quantum theory is called*quantum mechanics*. Relativistic quantum mechanics resulted from the extension of quantum mechanics to include the special theory of relativity.