Quantization (First, Second)
If there is a second quantization, presumably there is also a first quantization. The latter term refers to the ordinary application of the ► Schrödinger equation to physical objects characterized by ► wave functions, while the surrounding environment (such as an electromagnetic field) is treated classically. In second quantization the environment is treated quantum-mechanically — the field is quantized — and the wave function is considered as a dynamical system subject to quantization. To put it differently, one takes the wave function of an already quantized system and turns it into an ► operator.
The method of second quantization goes back to works of Paul A.M. Dirac and Pascual Jordan in 1927. Dirac used a kind of second quantization to the electromagnetic field by identifying the coefficients of the Fourier expansion of the field as photon ► creation and annihilation operators. He showed that there is a close connection between quantum fields and statistics, and derived in this way that photons obey ► Bose-Einstein statistics. Jordan went considerably further, in part alone and in part in works together with coauthors. Whereas Dirac restricted his approach to photons (► light quantum), Jordan quantized ► matter waves given by the Schrödinger equation, first non-relativistically and, with Eugene Paul Wigner in 1928, relativistically. Jordan's quantization could be performed in two ways, leading either to ► Bose-Einstein or ► Fermi-Dirac statistics. In the latter case it gave a quantum-mechanical justification of Pauli's ► exclusion principle.
KeywordsWave Function Annihilation Operator Exclusion Principle Matter Wave Light Quantum