Solving the spheroidal wave equation with s=3/2 by super-symmetric quantum mechanic

Abstract

In the paper, we use the method of super-symmetric quantum mechanics to study the spin-weighted spheroidal wave equation in the case of s=3/2. We first change the equation into Schrdinger's form, then calculate and derive the first four terms concerning E and super-potential W. we summarize the general formula of super-potential Wn and use mathematical induction to prove its correctness. In turn, this completely gives all the information about the ground eigenvalue and eigenfunction.