  We present series study of using the method of super-symmetric quantum
mechanics(SUSYQM) solving the spin-weighted spheroidal wave equation. In this
paper, we 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 summary the
general form for the n-th term of the super-potential, which is proved correct
by means of induction. We finally compute the ground eigenvalues and ground
eigenfunction. All the results may be of significative for studies of
electromagnetic radiation processes near rotating black holes and compute
radiation reaction in curved space-time.
