155 research outputs found

    New Investigation on the Spheroidal Wave Equations

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    Changing the spheroidal wave equations into new Schrodingerβ€²sform,thesuperβˆ’potentialexpandedintheseriesformoftheparameterdinger's form, the super-potential expanded in the series form of the parameter \alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the ground eigenfunctions of the spheroidal equations. But the shape-invariance property is not retained and the corresponding recurrence relations of the form (4) could not be extended from the associated Legendre functions to the case of the spheroidal functions

    The integral property of the spheroidal wave functions

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    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by the SUSQM; further it is not unreasonable to say they are non-solvable in some sense.Comment: This paper has been withdrawn by the authors.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
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