DOI: 10.12732/ijam.v38i2.1
HIGHER-ORDER HARMONIC OSCILLATOR
PERTURBED BY ALMOST PERIODIC POTENTIAL
Mohamed El Hammaji 1,§, Ilias Aarab 2
and Mohamed Ali Tagmouti 3
1,2,3 Abdelmalek Essaadi University
Faculty of Sciences
B.P 2121, Tetuan, MOROCCO
Abstract. We study the perturbation $L = H+V in L^2(R)$, where
$$ H = (-1)^l {\frac {d^{2l}}{dx^{2l}} + x^{2l}, l \in N^{*}$$
and $V$ is an almost periodic potential with uniformly continuous derivatives $V_1^(n)}$.
We assume that the eigenvalues of $L$ around $\lambda_k$ can be written in the form
$\lambda_k + \mu_k$. We establish an asymptotic formula for the fluctuation $\{\mu_k\}$,
which are determined by a transformation of $V$.
How
to cite this paper?
DOI: 10.12732/ijam.v38i2.1
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
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