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

Chinese Physics

Exact solutions for nonlinear Schr dinger equation in phase space: applications to Bose–Einstein condensate

Lu Jun

Published May 27, 2004• 6 citations
Publisher

Abstract

The stationary-state nonlinear Schrödinger equation, which models the dilute-gas Bose–Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The eigenfunctions in position and momentum spaces are obtained through the `Fourier-like' projection transformation from the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.

DOI
10.1088/1009-1963/13/6/005

Related papers

Attractive nonlinear Schrdinger equation and Bose-Einstein condensate in phase space

Shang Hong-ling

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of attractive nonlinear Schrdinger equation are solved, which models the Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the Fourier-like projection transformation from the phase-space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

Attractive Nonlinear Schrödinger Equation and Bose-Einstein Condensate in Phase Space

Jun Lu

In this paper, we solve the rigorous solutions of attractive nonlinear Schrödinger equation which models the Bose-Einstein condensate, within the framework of the quantum phase space representation established by Torres-Vega and Frederick. By means of the “Fourier-like” projection transformation, we obtain the eigenfunctions in position and momentum spaces from the phase space eigenfunctions. As an example, we discuss the eigenfunction with a hypersecant part.

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

Repulsive Nonlinear Schrödinger Equation and Bose-Einstein Condensate in Phase Space

Jun Lu, Yun Zhi Wang, Xiao Yun Mu

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of repulsive nonlinear Schrödinger equation are solved, which models the dilute-gas Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the “Fourier-like” projection transformation from the phase-space eigenfunctions. It shows that the wave-mechanics method in the phase-space representation could be extended to the nonlinear Schrödinger equations. The research provides the foundation for the approximate calculation in future.

Advanced materials research•Nov 1, 2011•0 citations

Theory of Quantum Phase Space and Bose-Einstein Condensate

Ping Wu

The quantum phase-space representation established by Torres-Vega and Frederick is discussed.It is described that the wave-functions are not unique in phase space.The rigorous solutions of nonlinear Schrdinger equation,which models the Bose-Einstein condensate,are solved within the framework of the quantum phase-space representation.The eigenfunctions in position and momentum spaces can be available through the Fourier-like projection transformation from the phase-space wave-functions.

Journal of Beijing Union University•Jan 1, 2006•0 citations

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

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
The stationary-state nonlinear Schrödinger equation, which models the dilute-gas Bose–Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The eigenfunctions in position and momentum spaces are obtained through the `Fourier-like' projection transformation from the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.
Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of repulsive nonlinear Schrödinger equation are solved, which models the dilute-gas Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the “Fourier-like” projection transformation from the phase-space eigenfunctions. It shows that the wave-mechanics method in the phase-space representation could be extended to the nonlinear Schrödinger equations. The research provides the foundation for the approximate calculation in future.
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.