Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

作者：Shi Yu Ren^*; Wang Xue Ling; Wang Guang Hui; Liu Cong Bo; Zhou Zhi Gang; Yang Hong Juan

来源：Frontiers of Physics, 2013, 8(3): 319-327.

DOI：10.1007/s11467-013-0332-x

• spin-1 Bose-Einstein condensate
• Gross-Pitaevskii equation
• homotopy analysis method
• analytical solution

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrodinger 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.

• 出版日期2013-6
• 单位西北师范大学