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The integral property of the spheroidal wave functions

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.

preprint2010arXivOpen access
Guihua TianShuquan Zhong
quant-ph
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Open access2 authors1 topic
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Guihua TianShuquan Zhong

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