球坐标系下三维谐振子的本征问题研究

Study on the Intrinsic Problem of Three Dimensional Harmonic Oscillator in Spherical Coordinate System

根据量子理论给出了球坐标系下角动量平方算符和三维谐振子哈密顿算符的本征值和本征波函数。结果表明球坐标系下三维谐振子本征波函数可以用级数递推关系给出,本征值和直角坐标系下得到的结果一样。

According to quantum theory,the eigenvalues and eigenwave functions of the angular momentum square operator and the Hamiltonian operator of the three-dimensional harmonic oscillator in spherical coordinate system are given.The results show that the eigenwave function of three dimensional harmonic oscillator in spherical coordinate system can be given by series recursion,and the eigenvalue is the same as that in rectangular coordinate system.