Wigner transform

by Claude Becker

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The Wigner transform [1], associates to every quantum operator  a real phase space function , its symbol, via
(1)
Its inverse, the Weyl transformation [2], gives a systematic way of associating quantum operators to classical distribution functions and is used in the Weyl quantization.
References:
  • [1]^ E.P. Wigner: On the quantum correction for thermodynamic equilibrium. In: Phys. Rev. 40, 1932, pp. 749–759.
  • [2]^ H.Weyl , "Quantenmechanik und Gruppentheorie", Zeitschrift für Physik, 46 (1927) pp. 1–46