On the eigenvalues of the spheroidal wave equation
Year: 2024
Type: article
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.
Author: Harald Schmid
Institution: Ostbayerische Technische Hochschule Amberg-Weiden
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,050
OpenAlex ID: W4405925401