Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the r and θ Dimensions of Spherical Polar Coordinates

Abstract

This article shows that in spherical polar coordinates, some noncentral separable potentials have supersymmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator as two important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in the r and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternative method to get the required results.