大学物理 ›› 2017, Vol. 36 ›› Issue (4): 6-11.doi: 10.16854 /j.cnki.1000-0712.2017.04.002

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一维谐振子势阱中二全同粒子的空间关联

刘志伟,孙保元   

  1. 兰州大学核科学与技术学院,甘肃兰州730000
  • 收稿日期:2016-09-09 修回日期:2016-11-03 出版日期:2017-04-20 发布日期:2017-04-20
  • 通讯作者: 孙保元,Email: sunby@ lzu.edu.cn
  • 作者简介:刘志伟( 1993—) ,男( 满族) ,辽宁省丹东市宽甸满族自治县人,兰州大学核科学与技术学院2016 级硕士研究生.
  • 基金资助:
    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)

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

LIU Zhi-wei,SUN Bao-yuan   

  1. School of Nuclear Science and Technology,Lanzhou University,Lanzhou,Gansu 730000,China
  • Received:2016-09-09 Revised:2016-11-03 Online:2017-04-20 Published:2017-04-20

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 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.

关键词: identical particles, exchange symmetry, one-dimensional harmonic oscillator potential, spatial relations.

Abstract: 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→0) tends to be zero while when anti-symmetrical,which will be useful for understanding the quantum effects induced by the exchange symmetry.

Key words:  identical particles, exchange symmetry, one-dimensional harmonic oscillator potential, spatial relations.