Generating all Wigner functions

Thomas Curtright, Tsuneo Uematsu, Cosmas Zachos

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasiprobability measure. The complete sets of Wigner functions necessary to expand all phase-space functions include off-diagonal Wigner functions, which may appear technically involved. Nevertheless, it is shown here that suitable generating functions of these complete sets can often be constructed, which are relatively simple, and lead to compact evaluations of matrix elements. New features of such generating functions are detailed and explored for integer-indexed sets, such as for the harmonic oscillator, as well as continuously indexed ones, such as for the linear potential and the Liouville potential. The utility of such generating functions is illustrated in the computation of star functions, spectra, and perturbation theory in phase space.

Original languageEnglish (US)
Pages (from-to)2396-2415
Number of pages20
JournalJournal of Mathematical Physics
Issue number6
StatePublished - Jun 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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