Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lecture notes in physics

A study of the analytical and local semiclassical Wigner distribution

Manuel Soares, Olivier Vallée, Charles de Izarra

Published Jan 1, 1999• 0 citations
Publisher
DOI
10.1007/bfb0105942

Related papers

A semiclassical approximation for the Wigner distribution function. Application to planar channeling

V.G. Novitzky

Physics Letters A•Apr 1, 1983•2 citations

The Wigner Distribution Function: Analytical Evaluation

Amalia Torre

Elsevier eBooks•Jan 1, 2005•1 citation

Equivalence between the two-dimensional real and analytic signal Wigner distributions

Zhu, y M, Françoise Peyrin, Robert Goutte

•Jan 1, 1989•9 citations

Semiclassical densities in phase space: Wigner's distribution function for thermodynamic equilibrium

H. J. Korsch

The quantum-mechanical joint (quasi-) density in phase space (the Wigner distribution) for thermodynamic equilibrium is studied in the semiclassical limit h(cross) to 0. The approximation is of an asymptotic (WKB) type and nonperturbative in character. The equilibrium phase-space distribution can be expressed in terms of classical paths satisfying certain well defined conditions. These paths are complex-valued, i.e. classically forbidden. The resulting semiclassical expression for the equilibrium Wigner phase-space density agrees with the exact quantum result for the analytical solvable case of harmonic potentials for all temperatures.

Journal of Physics A Mathematical and General•Jun 1, 1979•7 citations

Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

Gerhard Wilhelm Bund, M.C. Tijero

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit h --> 0 for fixed potential parameters.

arXiv:quant-ph/0304092•Journal of Physics A Mathematical and General•Mar 2, 2004•5 citations

Some remarks on the wigner distribution

Felix Alexandrovich Berezin

Theoretical and Mathematical Physics•Dec 1, 1973•25 citations
The quantum-mechanical joint (quasi-) density in phase space (the Wigner distribution) for thermodynamic equilibrium is studied in the semiclassical limit h(cross) to 0. The approximation is of an asymptotic (WKB) type and nonperturbative in character. The equilibrium phase-space distribution can be expressed in terms of classical paths satisfying certain well defined conditions. These paths are complex-valued, i.e. classically forbidden. The resulting semiclassical expression for the equilibrium Wigner phase-space density agrees with the exact quantum result for the analytical solvable case of harmonic potentials for all temperatures.
The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit h --> 0 for fixed potential parameters.