Computation of the eigenvalues for the angular and Coulomb spheroidal wave equation
Mathematical Physics
2022-11-30 v1 Numerical Analysis
Classical Analysis and ODEs
math.MP
Numerical Analysis
Abstract
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various Floquet solutions give rise to an entire function whose zeros are exactly the eigenvalues of the Coulomb spheroidal wave equation. This entire function can be calculated by means of a recurrence formula with arbitrary accuracy and low computational cost. Finally, one obtains an easy-to-use method for computing spheroidal eigenvalues and the corresponding eigenfunctions.
Keywords
Cite
@article{arxiv.2201.09506,
title = {Computation of the eigenvalues for the angular and Coulomb spheroidal wave equation},
author = {Harald Schmid},
journal= {arXiv preprint arXiv:2201.09506},
year = {2022}
}
Comments
23 pages, 5 figures