Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap |
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Authors: | Yu-Ren Shi Xue-Ling Wang Guang-Hui Wang Cong-Bo Liu Zhi-Gang Zhou Hong-Juan Yang |
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Institution: | 1. 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 Schrödinger 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. |
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