A New Method to Solve the Spheroidal Wave Equations

The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions' eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of all its terms is obtained. This means that the spheroidal problem is solved completely in the way for the ground eigen-value problem. The shape invariance property is proved retained for the super-potential and subsequently all the excited eigen-value problem could be solved. The results show that the spheroidal wave equations are integrable.