基于Gross-Pitaevskii能量泛函求解谐振势阱中玻色凝聚气体基态波函数  

Solution of the ground state wave function of Bose-condensed gas in a harmonic trap based on the Gross-Pitaevskii function

作　　者：徐志君[1,2] 施建青[1] 李珍[1] 蔡萍根[1] 

机构地区：[1]浙江工业大学应用物理系 [2]波谱与原子分子物理国家重点实验室,武汉430071

出　　处：《物理学报》2006年第7期3265-3271,共7页Acta Physica Sinica

基　　金：波谱与原子分子物理国家重点实验室开放基金(批准号:T152501);浙江省教育厅科研基金(批准号:20040599)资助的课题.~~

摘　　要：基于Gross-Pitaevskii(G-P)平均场能量泛函和变分方法,对囚禁在谐振势阱中的玻色凝聚气体,在T=0K时的基态波函数提出一种新解法.运用这一方法能得到基态波函数的解析表达式,求解出系统的化学势与凝聚原子数的关系等.其结果与Edwards和Dalfovo等人直接数值求解G-P方程所得到的结果相一致,并在Nas/a1大原子数N的极限条件下,与托马斯-费米近似模型的结论也趋向一致.该方法计算简单,而且能够进行解析处理.Based on the Gross-Pitaevskii（G-P） energy functional and variational method, we present a new method to find the ground state wave function for Bose-condensed gas in a harmonic trap at zero temperature. With this method we are able to find the analytic expression of ground state wave function and explore the relevant quantities, such as energy, chemical potential and so on. These results agree well with previous ground state numerical solutions of the G-P equation given by Daifovo et al. Under the large number of particles N limit for repulsive interaction, our results and Thomas-Fermi approximation model approach to reaching unanimity. This new method is simple compared to other methods used to solve numerically the G-P equation, and one can obtained the analytic and reliable results.

关 键 词：玻色凝聚气体 G-P泛函 谐振势阱 基态波函数 

分 类 号：O431.2[机械工程—光学工程]