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Journal of Atomic and Molecular Physics

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

Shang Hong-ling

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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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.