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

Exact classical limit of quantum mechanics: Central potentials and specific states

Adam J. Makowski

Published Jan 30, 2002• 17 citations
Publisher

Abstract

A derivation has been performed of some central potentials with no quantum correction to the Hamilton-Jacobi equation. In this exact limit of quantum mechanics, quantum trajectories identical to the classical ones are obtained. Interestingly, some of them are closed orbits. Applications of the found potentials in many areas of physics are also discussed.

DOI
10.1103/physreva.65.032103

Related papers

Bohr’s correspondence principle: The cases for which it is exact

Adam J. Makowski, K. Górska

Two-dimensional central potentials leading to the identical classical and quantum motions are derived and their properties are discussed. Some of zero-energy states in the potentials are shown to cancel the quantum correction $Q=(\ensuremath{-}{\ensuremath{\Elzxh}}^{2}/2m)\ensuremath{\Delta}R/R$ to the classical Hamilton-Jacobi equation. The Bohr's correspondence principle is thus fulfilled exactly without taking the limits of high quantum numbers, of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Elzxh}}0,$ or of the like. In this exact limit of $Q=0,$ classical trajectories are found and classified. Interestingly, many of them are represented by closed curves. Applications of the found potentials in many areas of physics are briefly commented.

Physical Review A•Dec 6, 2002•18 citations

Exact classical limit of quantum mechanics: Noncentral potentials and Ermakov-type invariants

Adam J. Makowski

Two-dimensional noncentral potentials are derived in the exact classical limit of quantum mechanics where the quantum correction to the classical Hamilton-Jacobi equation is canceled. It is then shown explicitly that there exist Ermakov-type invariants I for a large class of such potentials. Some of the invariants are found to be positive definite, $I>0,$ and for the other, we have found $I=0.$

Physical Review A•Aug 6, 2003•9 citations

The Classical Limit of Entropic Quantum Dynamics

Anthony Demme

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.

•May 1, 2017•5 citations

The classical limit of entropic quantum dynamics

Anthony Demme, Ariel Caticha

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ħ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.

arXiv:1612.01905•AIP conference proceedings•Jan 1, 2017•10 citations

On the Classical Limit of the Quantum Mechanics Based on the Hamilton-Jacobi Equation

Li-Feng Wang

Based on the Hamilton-Jacobi equation and the Bohm's quantum potential,it is pointed out that the classical limit of the quantum mechanics is the classical statistical mechanics.Through analyzing the Gaussian packet from two approaches,the perspective of the classical limit via the H-J equation is shown to be more profound than that via the Ehrenfest theorem.

Journal of Anyang Normal University•Jan 1, 2009•0 citations

The Classical Limit of Entropic Quantum Dynamics

Anthony Demme

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.

•May 1, 2017•0 citations
A derivation has been performed of some central potentials with no quantum correction to the Hamilton-Jacobi equation. In this exact limit of quantum mechanics, quantum trajectories identical to the classical ones are obtained. Interestingly, some of them are closed orbits. Applications of the found potentials in many areas of physics are also discussed.
Two-dimensional central potentials leading to the identical classical and quantum motions are derived and their properties are discussed. Some of zero-energy states in the potentials are shown to cancel the quantum correction $Q=(\ensuremath{-}{\ensuremath{\Elzxh}}^{2}/2m)\ensuremath{\Delta}R/R$ to the classical Hamilton-Jacobi equation. The Bohr's correspondence principle is thus fulfilled exactly without taking the limits of high quantum numbers, of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Elzxh}}0,$ or of the like. In this exact limit of Q=0,Q=0,Q=0, classical trajectories are found and classified. Interestingly, many of them are represented by closed curves. Applications of the found potentials in many areas of physics are briefly commented.
Two-dimensional noncentral potentials are derived in the exact classical limit of quantum mechanics where the quantum correction to the classical Hamilton-Jacobi equation is canceled. It is then shown explicitly that there exist Ermakov-type invariants I for a large class of such potentials. Some of the invariants are found to be positive definite, I>0,I>0,I>0, and for the other, we have found I=0.I=0.I=0.
The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.
The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ħ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.
The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.