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

arXiv:0912.2333

Examining the Wigner Distribution Using Dirac Notation

Frank Rioux

Published Dec 11, 2009• 0 citations
arXivHTMLPDF

Abstract

Expressing the Wigner distribution function in Dirac notation reveals its resemblance to a classical trajectory in phase space.
DOI
10.48550/arxiv.0912.2333

Related papers

Phase-space descriptions of operators and the Wigner distribution in quantum mechanics I. A Dirac inspired view

S. Chaturvedi, Elisa Ercolessi, Giuseppe Marmo +3 more

Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is marked by its economy, naturalness and more importantly, by its potential for extensions and generalisations to situations where the underlying configuration space is non Cartesian.

arXiv:quant-ph/0507053•Jul 6, 2005•2 citations

The Wigner Distribution

Robert F. O’Connell

In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function $W(q,p)$, the marginals of which yield the correct quantum probabilities for $q$ and $p$ separately \cite{wigner}. Its usefulness stems from the fact that it provides a re-expression of quantum mechanics in terms of classical concepts so that quantum mechanical expectation values are now expressed as averages over phase-space distribution functions. In other words, statistical information is transferred from the density operator to a quasi-classical (distribution) function.

arXiv:1009.4431•Sep 22, 2010•0 citations

Spreading of a free wave packet

Hai-Woong Lee

The spreading of a free wave packet and its relation to classical and quantum dynamics are examined. The phase-space formulation using the Wigner distribution function provides a convenient representation in which each phase point of the distribution follows a classical trajectory and the spreading occurs as a result of classical dynamics. A different formulation using a different phase-space distribution function, however, does not allow this simple interpretation of the spreading.

American Journal of Physics•May 1, 1982•18 citations

Classical distribution functions derived from Wigner distribution functions

Gerhard Wilhelm Bund

A mapping which relates the Wigner phase-space distribution function associated with a given stationary quantum-mechanical wavefunction to a specific solution of the time-independent Liouville transport equation is obtained. Two examples are studied.

Journal of Physics A Mathematical and General•Jul 7, 1995•4 citations

Quantum Mechanics in Phase Space

Ali M. Nassimi

The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.

arXiv:0706.0237•Jun 1, 2007•5 citations

Subtle nuances between quantum and classical regimes

Karin Wittmann Wilsmann, Erick R. Castro, I. Roditi +2 more

This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the principle of uniform semiclassical condensation of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes.

arXiv:2411.07373•Chaos An Interdisciplinary Journal of Nonlinear Science•Apr 1, 2025•2 citations
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function W(q,p)W(q,p)W(q,p), the marginals of which yield the correct quantum probabilities for qqq and ppp separately \cite{wigner}. Its usefulness stems from the fact that it provides a re-expression of quantum mechanics in terms of classical concepts so that quantum mechanical expectation values are now expressed as averages over phase-space distribution functions. In other words, statistical information is transferred from the density operator to a quasi-classical (distribution) function.
This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the principle of uniform semiclassical condensation of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes.