Quantum mechanics is the branch of physics treating atomic and subatomic systems and their interaction with radiation. It is based on the observation that all forms of energy are released in discrete units or bundles called “quanta”. Remarkably, quantum theory typically permits only probable or statistical calculation of the observed features of subatomic particles, understood in terms of wavefunctions.

The Schrödinger equation plays the role in quantum mechanics that Newton’s laws and conservation of energy serve in classical mechanics—i.e., it predicts the future behavior of a dynamic system—and is a wave equation that is used to solve for wavefunctions.

For example, the light, or electromagnetic radiation emitted or absorbed by an atom has only certain frequencies (or wavelengths), as can be seen from the line spectrum 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, 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. The photoelectric effectfurther confirmed the quantization of light.

In 1924, Louis de Broglie proposed that not only do light waves sometimes exhibit particle-like properties, but particles may also exhibit wave-like properties. 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. 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. Quantum mechanics was combined with the theory of relativity in the formulation of Paul Dirac. Other developments include quantum statistics, quantum electrodynamics, concerned with interactions between charged particles and electromagnetic fields; and its generalization, quantum field theory.