Spin-weighted spheroidal equation in the case of s=1

We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s=1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen-functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.