Arnolídís analytic perturbation for the polar equation

Samuel Dillon

Abstract

Based on the paper of Arnolíd [1] on the problems of Mathieu type,
we suggest a modified Feynmann diagram technique to assist in solving
problems of the form Aεy = (I + εV )−1A0y = λy. We then use this
method to calculate eigenvalues and eigenfunctions to the polar problem,
−
d2y
dx2 = λ(1 + ε cos x)y,
with the quasiperiodic boundary condition on [0, 2π].

Keywords
Perturbation, Feynmann Disgram, polar equation

Math Review Classification
Primary 81Q15 ; Secondary 47N20

Last Updated
September 5, 2006

Length
14 pages

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