Abstract: This article shows that in spherical polar coordinates, the ring-shaped oscillator potential has supersymmetry and shape invariance in the r dimension and in the θ dimension, it obtains the energy eigenvalues and energy eigenfunctions of this potential.

Key words: ring-shaped oscillator, supersymmetry, shape invariance, energy eigenvalue, energy eigenfunction

摘要： 证明了在球极坐标下环形振子势在 r维和 θ维具有超对称性和形不变性，得到了该势的能量本征值和能量本征函数。

关键词: 环形振子, 超对称性, 形不变性, 能量本征值, 能量本征函数