### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 2396-2415 |

Number of pages | 20 |

Journal | Journal of Mathematical Physics |

Volume | 42 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2001 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Mathematical Physics*,

*42*(6), 2396-2415. https://doi.org/10.1063/1.1366327

**Generating all Wigner functions.** / Curtright, Thomas; Uematsu, Tsuneo; Zachos, Cosmas.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 42, no. 6, pp. 2396-2415. https://doi.org/10.1063/1.1366327

}

TY - JOUR

T1 - Generating all Wigner functions

AU - Curtright, Thomas

AU - Uematsu, Tsuneo

AU - Zachos, Cosmas

PY - 2001/6

Y1 - 2001/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035534440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035534440&partnerID=8YFLogxK

U2 - 10.1063/1.1366327

DO - 10.1063/1.1366327

M3 - Article

AN - SCOPUS:0035534440

VL - 42

SP - 2396

EP - 2415

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -