Numerical solution for the Gross–Pitaevskii equation

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• 作者：Wei Hua ; Xueshen Liu and Peizhu Ding
• 关键词：Gross–Pitaevskii equation ; stationary solution ; Bose–Einstein Condensate
• 刊名：Journal of Mathematical Chemistry
• 出版年：2006
• 出版时间：October, 2006
• 年：2006
• 卷：40
• 期：3
• 页码：243-255
• 全文大小：158 KB
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

We solve the time-independent Gross–Pitaevskii (GP) equation which describes the dilute Bose-condensed atoms in harmonic trap at zero temperature by symplectic shooting method (SSM). Both the repulsive nonlinearity and the attractive nonlinearity cases are studied, and the bound state eigenvalues as well as the corresponding wavefunctions are evaluated. We also present the numerical results by studying the time-dependent GP equation, and comparisons are made between the results obtained by the time-independent approach and the time-dependent approach.