用F-G-H方法研究玻色-爱因斯坦凝聚体基态性质

用F-G-H方法数值求解描述BEC凝聚体的非线性薛定谔方程-Gross-Pitaevskii方程.研究总粒子数、粒子间相互作用、谐振频率和一般幂指数外势对玻色凝聚体粒子数密度分布、基态能量的影响.结果表明,增大幂指数外势、谐振频率,降低粒子间的排斥作用会增加凝聚体中心的粒子数密度、缩小凝聚体半径;增大总粒子数、谐振频率、粒子间的排斥作用和幂指数外势的指数会增大体系的基态能量;随着总粒子数增大,数值结果与托马斯-费米近似结果渐趋一致,托马斯-费米近似在大粒子数条件下是一种较好的近似方法,在粒子数有限时,结果与真实情形偏差较大,应采用数值解法.

Ground State of Bose-Einstein Condensation in F-G-H Method

We study distribution of particles in Bose-Einstein condensation and ground state energy of condensate by solving a G-P equation with Fourier-Grid-Hamiltonian(F-G-H) method. It is shown that particle density in condensate center increases and radius of condensate decreases as intensity of power-law potential or frequency of harmonic potential is increased or repulsive interaction between particles is decreased. The ground state energy of BEG increases with increasing of total particle number, repulsive interaction between particles, frequency of harmonic potential or intensity of power-law potential. Thomas-Fermi approximation results approximate to numerical results as particle number increases. It is shown that Thomas-Fermi approximation is a good method with large particle numbers. For less particle numbers, numerical method should be used.