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

Physica Scripta

Classical Structures in the Husimi Distributions of Stationary States for H2and HCl Molecules in the Morse Potential

Adélcio C. Oliveira, Maria Carolina Nemes

Published Jan 1, 2001• 4 citations
Publisher

Abstract

The Morse potential is used to obtain analytical solutions of the lowest stationary states of the H 2 and HCl molecules. We construct the Husimi distributions for several states and show that the phase space distribution of these states retain several features of its classical limit. Similar results have been reported for one dimensional systems. For the specific case of the central potentials, we show how to treat the angular variables in a consistent way.

DOI
10.1238/physica.regular.064a00279

Related papers

On the zeros of the Husimi distribution

H. J. Korsch, Christopher Müller, H Wiescher

The basic features of the zeros of the Husimi phase-space density of a quantum eigenstate are discussed. It is demonstrated that some special properties of the harmonic oscillator related to the number of zeros and their location within the classical energy shell are not valid for anharmonic potentials, as illustrated by numerical examples for the Morse oscillator. Also discussed is the distribution of zeros in quantum Poincaré sections for systems with two degrees of freedom.

Journal of Physics A Mathematical and General•Oct 21, 1997•72 citations

Husimi representation for stationary states

John E. Harriman, Mark E. Casida

Abstract This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1993•27 citations

Semiclassical Husimi Function of Simple and Chaotic Systems

Adélcio C. Oliveira

We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.

Journal of Modern Physics•Jan 1, 2012•7 citations

Quantum mechanics on a circle: Husimi phase-space distributions and semiclassical coherent state propagators

B Bahr, H J Korsch

We discuss some basic tools for an analysis of one-dimensional quantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states, are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros. Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.

arXiv:quant-ph/0611116•Journal of Physics A Mathematical and Theoretical•Mar 20, 2007•10 citations

Quantum surfaces of section for the diamagnetic hydrogen atom: Husimi functions versus Wigner functions

Paul A. Dando, T. S. Monteiro

We compare quantum phase space distributions of individual quantum states of the diamagnetic hydrogen atom obtained by means of Wigner functions with those given by Husimi functions. The comparison is carried out at effective h(cross) approximately 0.035 and at a fixed scaled energy ( epsilon =-0.316) which corresponds to an especially interesting mixed classical phase-space structure. The object of the comparison is to establish which of the two distributions best correlates with the classical Poincare surface of section for a representative set of single states. As expected, the states investigated display the strongest positive intensity on a single local invariant phase-space structure (such as a scar or torus) and at this level there is little difference between the Husimi and the Wigner function. However the weak structures (fringes of the Wigner function or zeros of the Husimi function) are shown here to be radically different for the Wigner relative to the Husimi representation. In both cases the weak structures permeate all of phase space. In addition they show different character for integrable and chaotic dynamics and so reflect the global structure of phase-space to a much greater extent than the localized strong structure. The Wigner functions of selected states are shown to have additional dynamically significant structures which are not apparent in the Husimi functions. These include negative intensity features seen in the Wigner-but not the Husimi-functions which are very well correlated with structures of the classical Poincare surfaces of section. Despite its complex oscillatory nature the Wigner function delineates better classical features, for example showing the outline of islands of stability avoided by states supported by chaotic regions with greater sharpness than the Husimi function.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 14, 1994•22 citations

The Husimi distribution function and superposition of q-harmonic oscillator stationary states

Natig M. Atakishiyev, E. I. Jafarov, A. M. Jafarova +1 more

We study a superposition of four stationary states of the q-deformed quantum harmonic oscillator in phase space, through the Husimi quasi-distribution function. This function is analytically computed and it consists of 16 parts, which are explicitly given in terms of q-shifted factorials. Our results are consistent with the known observation that the smoothing of the Wigner quasi-probability distribution through a filter of a size larger than h-bar restricts the appearance of any sub-Planck structures when q -> 0.

•Jan 1, 2014•0 citations
The Morse potential is used to obtain analytical solutions of the lowest stationary states of the H 2 and HCl molecules. We construct the Husimi distributions for several states and show that the phase space distribution of these states retain several features of its classical limit. Similar results have been reported for one dimensional systems. For the specific case of the central potentials, we show how to treat the angular variables in a consistent way.
Abstract This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.
We discuss some basic tools for an analysis of one-dimensional quantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states, are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros. Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.
We compare quantum phase space distributions of individual quantum states of the diamagnetic hydrogen atom obtained by means of Wigner functions with those given by Husimi functions. The comparison is carried out at effective h(cross) approximately 0.035 and at a fixed scaled energy ( epsilon =-0.316) which corresponds to an especially interesting mixed classical phase-space structure. The object of the comparison is to establish which of the two distributions best correlates with the classical Poincare surface of section for a representative set of single states. As expected, the states investigated display the strongest positive intensity on a single local invariant phase-space structure (such as a scar or torus) and at this level there is little difference between the Husimi and the Wigner function. However the weak structures (fringes of the Wigner function or zeros of the Husimi function) are shown here to be radically different for the Wigner relative to the Husimi representation. In both cases the weak structures permeate all of phase space. In addition they show different character for integrable and chaotic dynamics and so reflect the global structure of phase-space to a much greater extent than the localized strong structure. The Wigner functions of selected states are shown to have additional dynamically significant structures which are not apparent in the Husimi functions. These include negative intensity features seen in the Wigner-but not the Husimi-functions which are very well correlated with structures of the classical Poincare surfaces of section. Despite its complex oscillatory nature the Wigner function delineates better classical features, for example showing the outline of islands of stability avoided by states supported by chaotic regions with greater sharpness than the Husimi function.
We study a superposition of four stationary states of the q-deformed quantum harmonic oscillator in phase space, through the Husimi quasi-distribution function. This function is analytically computed and it consists of 16 parts, which are explicitly given in terms of q-shifted factorials. Our results are consistent with the known observation that the smoothing of the Wigner quasi-probability distribution through a filter of a size larger than h-bar restricts the appearance of any sub-Planck structures when q -> 0.