Tables of Eigenvalues of the Wave Equation in Prolate Spheroidal Coordinates

摘要

The wave equation in prolate spheroidal coordinates was separated into radial and angle functions. The differential equation satisfied by the angle functions was written in the form of an eigenvalue problem, that is, as a linear operator operating on eigenfunctions to yield the same eigenfunctions multiplied by corresponding eigenvalues. The eigenvalues were numerically calculated by use of Galerkin's method. This method reduces to the evaluation of the characteristic roots of a large matrix. An 80 by 80 matrix is chosen and a detailed calculation on a high-speed computer leads to a tabulation. The table of prolate eigenvalues published here has the range m = 0, 1, 2; l = m (1) m + 49; h = 0.1 (0.1) 0.9, 1.0 (0.2) 8.0, 10.0, 20.0 (20.0) 100.0. The precision is 21 significant figures. (Author)