Variational Solutions for Eigenvalues of Single and Coupled LaméEquations

摘要

The approach of Taylor&Arscott for the evaluation of eigenvalues for singly periodic Laméequations is modified by truncating the infinite matrix representing Hill's equation to finite size. For two separate Laméequations with a common separation constant A and a linear relation between their eigenvalues, A is found by Newton's method; the required derivatives are expressed as expectation values. Truncation to five or six rows is adequate for most practical purposes. The results of Taylor for the delta wing problem are verified for small A, but for larger values of A perturbation expansions are shown to lead to quantitatively and qualitatively erroneous result