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
Generating all Wigner functions. / Curtright, Thomas; Uematsu, Tsuneo; Zachos, Cosmas.
In: Journal of Mathematical Physics, Vol. 42, No. 6, 06.2001, p. 2396-2415.Research output: Contribution to journal › Article
}
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 -