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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

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Front. Phys.    2013, Vol. 8 Issue (3) : 319-327    https://doi.org/10.1007/s11467-013-0332-x
RESEARCH ARTICLE
Analytical solutions for the spin-1 Bose–Einstein condensate in a harmonic trap
Yu-Ren Shi (石玉仁,), Xue-Ling Wang (王雪玲), Guang-Hui Wang (王光辉), Cong-Bo Liu (刘丛波), Zhi-Gang Zhou (周志刚), Hong-Juan Yang(杨红娟)
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
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Abstract

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross–Pitaevskii equations, a set of nonlinear Schr?dinger equation used in simulation of spin-1 Bose–Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.
Keywords spin-1 Bose–Einstein condensate      Gross–Pitaevskii equation      homotopy analysis method      analytical solution     
Corresponding Author(s): Yu-Ren Shi (石玉仁),Email:syr317@163.com   
Issue Date: 01 June 2013
 Cite this article:   
Yu-Ren Shi (石玉仁),Xue-Ling Wang (王雪玲),Guang-Hui Wang (王光辉), et al. Analytical solutions for the spin-1 Bose–Einstein condensate in a harmonic trap[J]. Front. Phys. , 2013, 8(3): 319-327.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-013-0332-x
https://academic.hep.com.cn/fop/EN/Y2013/V8/I3/319
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