  The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used
to study whether the spheroidal equations have the shape-invariance property.
Expanding the super-potential term by term in the parameter alpha and solving
it, we find that the superpotential loses its shape-invariance property upon to
the second term. This first means that we could not solve the spheroidal
problems by the SUSQM; further it is not unreasonable to say they are
non-solvable in some sense.
