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

Wave Mechanics in Quantum Phase Space: Harmonic Oscillator

Jun Lu

Published Jan 1, 2004• 4 citations
Publisher

Abstract

In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the three-dimensional isotropic harmonic oscillator in rectangular and spherical coordinate systems, and discuss the relationship between the eigenfunctions of the two coordinate systems. We also extend the "Fourier-like" projection transformations of the phase-space wave function to three-dimensional systems, and obtain the eigenfunctions in position and momentum representation through the transformations of the eigenfunction in the phase-space representation.

DOI
10.1238/physica.regular.069a00084

Related papers

Rigorous Solution of Harmonic Oscillator in Quantum Phase-space Representation

Yunzhi Wang

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick,the rigorous solutions of stationary Schro¨dinger equation for one-dimensional harmonic oscillator are solved with the methods of matrix mechanics and wave mechanics respectively.It is showed that the matrix mechanics and the wave mechanics are equivalent in phase space.The eigenfunctions in position and momentum spaces can be obtained through the Fourier-like projection transformation from the phase-space eigenfunction.

Journal of Guangxi Normal University•Jan 1, 2007•0 citations

One-Dimensional Harmonic Oscillator in Quantum Phase Space

Jun Lu, Xue Mei Wang, Ping Wu

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

Applied Mechanics and Materials•Oct 24, 2011•0 citations

Wave mechanics in quantum phase space: hydrogen atom

Jun Lu

The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The Fourier-like projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.

Progress in Natural Science Materials International•Feb 1, 2007•0 citations

Phase-Space Wave Functions of Harmonic Oscillator in Nanomaterials

Jun Lu

In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator in nanomaterials within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the harmonic oscillator. We also discuss the character of wave function and the “Fourier-like” projection transformations in phase space.

Advanced materials research•May 12, 2011•0 citations

Theory of Quantum Phase Space and Rigorous Solution of Hydrogen Atom

Jun Lu

The method of wave mechanics in the quantum phase-space representation established by TorresVega and Frederick is introduced.The Fourier-like projection transformation between phase-space representation and position or momentum representation is discussed.The rigorous solutions of stationary Schrdinger equation for one-dimensional hydrogen atom are obtained.It is described that the wave functions are not unique in phase space.

Journal of Hebei Normal University•Jan 1, 2007•0 citations

Results and Relationship on the Three-Dimensional Isotropic Harmonic Oscillator in the Two Different Coordinate Systems

FU Xi-jin

Based on the schrodinger function,the eigenfunctions and eigenvalue for three–dimensional isotropic harmonic oscillator were derived in Cartesian coordinate system and in Spherical coordinate system respectively,the relationship between the two eigenfunctions were obtained.

Journal of Gansu Lianhe University•Jan 1, 2010•0 citations
In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the three-dimensional isotropic harmonic oscillator in rectangular and spherical coordinate systems, and discuss the relationship between the eigenfunctions of the two coordinate systems. We also extend the "Fourier-like" projection transformations of the phase-space wave function to three-dimensional systems, and obtain the eigenfunctions in position and momentum representation through the transformations of the eigenfunction in the phase-space representation.
Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick,the rigorous solutions of stationary Schro¨dinger equation for one-dimensional harmonic oscillator are solved with the methods of matrix mechanics and wave mechanics respectively.It is showed that the matrix mechanics and the wave mechanics are equivalent in phase space.The eigenfunctions in position and momentum spaces can be obtained through the Fourier-like projection transformation from the phase-space eigenfunction.
The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The Fourier-like projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.