11,748 research outputs found

    The integral property of the spheroidal wave functions

    Full text link
    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by the SUSQM; further it is not unreasonable to say they are non-solvable in some sense.Comment: This paper has been withdrawn by the authors. In later study, we found the conclusion is wrong in some wa