Advertisement

Quantization (First, Second)

  • Helge Kragh

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.

Keywords

Wave Function Annihilation Operator Exclusion Principle Matter Wave Light Quantum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Primary Literature

  1. 1.
    P. A. M. Dirac: The Quantum Theory of the Emission and Absorption of Radiation. Proceedings of the Royal Society of London A 114, 243–265 (1927)ADSGoogle Scholar
  2. 2.
    P. Jordan: Über eine neue Begründung der Quantenmechanik. Zeitschrift für Physik 44, 1–25 (1927)CrossRefADSGoogle Scholar
  3. 3.
    V. Fock: Konfigurationsraum und zweite Quantelung. Zeitschrift für Physik 75, 622–647 (1932)zbMATHCrossRefADSGoogle Scholar

Secondary Literature

  1. 4.
    O. Darrigol: The origin of quantized matter waves. Historical Studies in the Physical Sciences 16, 197–253 (1986)Google Scholar
  2. 5.
    H. D. Zeh: There Is no “first” quantization. Physics Letters A 309, 329–334 (2003)ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Helge Kragh
    • 1
  1. 1.University of AarhusDenmark

Personalised recommendations