Analytical Solutions to the Time-Independent Gross-Pitaevskii Equation with a Harmonic Trap
SHI Yu-Ren** , WANG Guang-Hui, LIU Cong-Bo, ZHOU Zhi-Gang, YANG Hong-Juan
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070
Abstract ：We try to find the analytical solutions to the time-independent Gross-Pitaevskii equation, a nonlinear Schr?dinger equation used in the simulation of Bose–Einstein condensates trapped in a harmonic potential. Both the homotopy analysis method and the Galerkin spectral method are applied. We investigate the one-dimensional case and obtain the approximate analytical solutions successfully. Comparison between the analytical solutions and the numerical solutions has been made. The results indicate that they agree very well with each other when the atomic interaction is not too strong.
收稿日期: 2012-05-22
出版日期: 2012-11-28
:
03.65.Ge
(Solutions of wave equations: bound states)
03.75.Hh
(Static properties of condensates; thermodynamical, statistical, and structural properties)
02.70.Dh
(Finite-element and Galerkin methods)
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2012, Vol. 29 
