Study of the Spin-weighted Spheroidal Wave Equation in the Case of s=3/2

In this paper, we use the means of super-symmetric quantum mechanics to study of the Spin-weighted Spheroidal Wave in the case of s=3/2. We obtain some interesting results: the first-five terms of the super-potential, the general form of the super-potential. The ground eigen-function and eigenvalue of the equation are also given. According these results, we make use of the shape invariance property to compute the exited eigenvalues and eigen-functions. These results help us to understand the Spin-weighted Spheroidal Wave and show that it is integral.