| Based on the paper of Arnol’d [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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