中文摘要：

从全同粒子的多体波函数对称性理论出发,推导出了全同粒子的密度分布函数,并精确地计算了不同温度下,一维简谐势阱中无相互作用的玻色子体系的密度分布。发现在低温下,尤其是在临界温度附近,一维玻色子的密度分布呈现出类似于玻色-爱因斯坦凝聚的效应。同时,在高温条件下,采用半经典的方法,利用玻尔兹曼分布计算了玻色子的密度分布,并且和玻色分布计算出的结果进行了对比,发现随着温度的升高,两种密度分布渐渐趋于一致。

英文摘要：

Starting from the symmetric multi-body wave function theory of identical particles, the general expression of the single particle density profile is obtained. And we numerically calculate the single particle density profile for non-interacting Boson system confined in one dimension harmonic potential under differ- ent temperatures. The density profile is strikingly narrow down when the temperature goes down below the critical temperature To. This phenomenon is similar to Bose-Einstein condensation. At high tempera- ture, a comparison of Bose distribution and Boltzmann distribution is explored. And the density profile for the Bose distribution become nearly the same as the density profile for Boltzmann distribution when tem- perature goes very high.