While the theory of relativity was largely the work of one man, Albert Einstein, 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 radiation in 1900 by Max Planck, who proposed that the energies of any harmonic oscillator (see harmonic motion), 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 6.63×10^{ - 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. Following the discovery of the nuclear atom by Rutherford (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, the final mathematical formulation of the quantum theory, was developed during the 1920s. In 1924, Louis de Broglie 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 and L. H. Germer, who observed diffraction 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 (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 (1928), which, in addition, predicted the existence of antiparticles. A particularly important discovery of the quantum theory is the uncertainty principle, enunciated by Heisenberg 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) and in another by Dirac and Enrico Fermi (the Fermi-Dirac statistics); quantum electrodynamics, concerned with interactions between charged particles and electromagnetic fields; its generalization, quantum field theory; and quantum electronics.

- Introduction
- Relationship of Energy and Matter
- Dual Nature of Waves and Particles
- Evolution of Quantum Theory
- Bibliography

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.