Exact solutions for nonlinear Schrödinger equation in phase space: applications to Bose－Einstein condensate
Lu Jun (陆军)
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China; Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
Abstract The stationary-state nonlinear Schr?dinger 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.
Received: 04 July 2003
Revised: 04 November 2003
Accepted manuscript online:
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