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arXiv · 2402.07133

On the eigenvalues of the spheroidal wave equation

Harald Schmid
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Abstract

This paper presents some new results on the eigenvalues of the spheroidal wave equation. We study the angular and Coulomb spheroidal wave equation as a special case of a more general linear Hamiltonian system depending on three parameters. We prove that the eigenvalues of this system satisfy a first-order quasilinear partial differential equation with respect to the parameters. This relation offers a new insight on how the eigenvalues of the spheroidal wave equation depend on the spheroidal parameter. Apart from analytical considerations, the PDE we obtain can also be used for a numerical computation of spheroidal eigenvalues.

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Harald Schmid. 2024-02-11. On the eigenvalues of the spheroidal wave equation. https://doi.org/10.1016/j.jde.2024.12.032

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