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.

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.