一维谐振子势阱中二全同粒子的空间关联  

Spatial correlations of two identical particles in one-dimensional harmonic oscillator potential

作　　者：刘志伟[1] 孙保元[1] 

机构地区：[1]兰州大学核科学与技术学院,甘肃兰州730000

出　　处：《大学物理》2017年第4期6-11,共6页College Physics

基　　金：兰州大学研究生课程建设项目资助;中央高校基本科研业务费专项资金资助(lzujbky-2016-30)

摘　　要：针对一维谐振子势阱中由两个全同粒子组成的体系,假设其空间波函数分别具有以下3种交换对称性:1)没有交换对称性,2)对于交换是反对称情况,3)对于交换是对称情况,讨论了二粒子空间相对位置的分布概率.并由此将量子力学教材中自由粒子情况下的结论推广至一维谐振子束缚态情形,即两个全同粒子无论是处于自由态还是束缚态,在空间波函数交换对称的情况下,两个粒子靠拢的概率最大,而交换反对称情况下,两个粒子靠近(r→0)的概率趋于零.论文结论有助于加深对量子力学中全同粒子交换对称性及其物理效应的理解.Inspired by a sample question in the textbook of quantum mechanics, the spatial correlations of two identical particles in the one-dimensional harmonic oscillator potential are discussed, where the exchange symmetry of wave function is assumed to be classical, symmetrical and anti-symmetrical, respectively. It is found that the results for free particles still hold for the one-dimensional harmonic oscillator bound states, namely, when the exchange symmetry is symmetrical, the two particles tend to draw close each other, the probability of two particles approaching each other（r→O） tends to be zero while when anti-symmetrical, which will be useful for understanding the quantum effects induced by the exchange symmetry.

关 键 词：全同粒子 交换对称性 一维谐振子势 空间关联 

分 类 号：O413.1[理学—理论物理]