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

Physical Review A

Correspondence between quantum and classical descriptions for free particles

Xin Huang

Published Aug 21, 2008• 9 citations
Publisher

Abstract

We define the condition of the quasiclassical state of free particles, which is useful in the approximate treatment of quantum systems. Then we introduce classical pure ensembles. Their states are represented using distribution functions on phase space. We compare distribution functions of classical pure ensembles and Wigner distribution functions of quasiclassical states for free particles and draw two conclusions: (i) A wave function does not describe an individual particle but a classical pure ensemble. (ii) Given a quasiclassical wave function, we can tell which classical pure ensemble is described by it.

DOI
10.1103/physreva.78.022109

Related papers

Classical Limit of Quantum Mechanics

Xiang-You Huang

Because of the use of different limiting procedures, there are two conflict conclusions on wave function. One is that a wave function can describe a single particle and the other is that it can only describe an ensemble in the classical limit. In this paper the limiting procedures have been compared. We put the synthesized limit n→∞, →0 but keep E(n, ) to be the actual measured value of energy. Under this limit condition, we can not only prove that a wave function can only describe an ensemble, but also can make clear the dynamical behavior of the particles of the ensemble. Calculations show that the reason why quantum mechanics cannot describe a particle is not because of the motion equation but because of the definition of state for the particle.

Science in China Series A-Mathematics Physics Astronomy & Technological Science•Feb 20, 1993•1 citation

Wigner phase-space distribution as a wave function

Denys I. Bondar, Renán Cabrera, Dmitry V. Zhdanov +1 more

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman--von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

arXiv:1202.3628•Physical Review A•Nov 11, 2013•50 citations

On the Quantum-Classical Character of the Quantum Wavefunction of Material Particles

Daniela Dragoman

We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum particle between the quantum and classical realms. Accordingly, classical and quantum mechanics should not be treated separately, a unified description in terms of the Wigner distribution function being possible. Although defined on classical phase space coordinates, the Wigner distribution function accommodates the nonlocalization property of quantum systems, and leads to both the Schrodinger equation for the quantum wavefunction and to the definition of position and momentum operators.

arXiv:quant-ph/0604087•Annales de la fondation Louis de Broglie/Annales de la Fondation Louis de Broglie•Apr 12, 2006•0 citations

What object does the wave function describe?

Yuri A. Rylov

It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.

arXiv:physics/0405117•May 21, 2004•5 citations

The Domain of the Quantum Matter Wave

Bruce Mills

Abstract In quantum mechanics a particle is represented by a complex wave function. This is similar to the classical description of a distributed particle by a real valued density function. However, while classically the combined density of multiple particles can be decomposed into individual densities; the wave function of a multi-particle system can not always be decomposed into wave functions for the individual particles. Hence the classical assumption that density is a property of physical space, which is only possible because of the special topology of classical configuration space, does not work for quantum systems.

Zeitschrift für Naturforschung A•Feb 1, 2001•1 citation

Measurement of the Wigner Function

Antoine Royer

An operational procedure is given for determining experimentally, in principle at least, the Wigner function for an ensemble of particles. This manner of "measuring" a quantum state, whether pure or mixed, via its Wigner function, seems the simplest possible, and closely parallels the method one might use in classical mechanics to determine a (true) phase-space probability density.

Physical Review Letters•Dec 16, 1985•76 citations
We define the condition of the quasiclassical state of free particles, which is useful in the approximate treatment of quantum systems. Then we introduce classical pure ensembles. Their states are represented using distribution functions on phase space. We compare distribution functions of classical pure ensembles and Wigner distribution functions of quasiclassical states for free particles and draw two conclusions: (i) A wave function does not describe an individual particle but a classical pure ensemble. (ii) Given a quasiclassical wave function, we can tell which classical pure ensemble is described by it.
Because of the use of different limiting procedures, there are two conflict conclusions on wave function. One is that a wave function can describe a single particle and the other is that it can only describe an ensemble in the classical limit. In this paper the limiting procedures have been compared. We put the synthesized limit n→∞, →0 but keep E(n, ) to be the actual measured value of energy. Under this limit condition, we can not only prove that a wave function can only describe an ensemble, but also can make clear the dynamical behavior of the particles of the ensemble. Calculations show that the reason why quantum mechanics cannot describe a particle is not because of the motion equation but because of the definition of state for the particle.
We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman--von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum particle between the quantum and classical realms. Accordingly, classical and quantum mechanics should not be treated separately, a unified description in terms of the Wigner distribution function being possible. Although defined on classical phase space coordinates, the Wigner distribution function accommodates the nonlocalization property of quantum systems, and leads to both the Schrodinger equation for the quantum wavefunction and to the definition of position and momentum operators.
It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.
Abstract In quantum mechanics a particle is represented by a complex wave function. This is similar to the classical description of a distributed particle by a real valued density function. However, while classically the combined density of multiple particles can be decomposed into individual densities; the wave function of a multi-particle system can not always be decomposed into wave functions for the individual particles. Hence the classical assumption that density is a property of physical space, which is only possible because of the special topology of classical configuration space, does not work for quantum systems.