Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillator

Abstract

In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation and investigate how the Hölder constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.

19 pages