中国物理B ›› 2004, Vol. 13 ›› Issue (6): 811-816.doi: 10.1088/1009-1963/13/6/005

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

陆军   

  1. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China; Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
  • 收稿日期:2003-07-04 修回日期:2003-11-04 出版日期:2004-07-05 发布日期:2005-07-05

Exact solutions for nonlinear Schrödinger equation in phase space: applications to Bose－Einstein condensate

Lu Jun (陆军)   

  1. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China; Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
  • Received:2003-07-04 Revised:2003-11-04 Online:2004-07-05 Published:2005-07-05

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摘要： 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.

关键词: nonlinear equation, phase space, Bose－Einstein condensate

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.

Key words: nonlinear equation, phase space, Bose－Einstein condensate

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
03.65.Ge (Solutions of wave equations: bound states) 03.65.Fd (Algebraic methods) 03.75.Kk (Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)