Spectral asymptotics of harmonic oscillator perturbed by bounded potential

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dc.creatorKlein, M.
dc.creatorKorotyaev, E.
dc.creatorPokrovski, A.
dc.date2003-12-24
dc.date.accessioned2026-07-07T06:20:48Z
dc.date.available2026-07-07T06:20:48Z
dc.descriptionConsider the operator $ T=-{d^2dx^2}+x^2+q(x)$ in $L^2(\mathbb{R})$, where real functions $q$, $q'$ and $\int_0^xq(s)ds$ are bounded. In particular, $q$ is periodic or almost periodic. The spectrum of $T$ is purely discrete and consists of the simple eigenvalues $\{μ_n\}_{n=0}^\infty$, $μ_n<μ_{n+1}$. We determine their asymptotics $μ_n = (2n+1) + (2π)^{-1}\int_{-π}^πq(\sqrt{2n+1}\sinθ)dθ+ O(n^{-1/3})$.
dc.descriptionLaTeX, 39 pages, 2 postscript figures
dc.identifierhttps://arxiv.org/abs/math-ph/0312066
dc.identifierhttp://arxiv.org/abs/math-ph/0312066
dc.identifierAnnales Henri Poincare, V.6, No.4, pp.747-789,2005.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95417
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject34L20 (Primary) 47N50 (Secondary)
dc.titleSpectral asymptotics of harmonic oscillator perturbed by bounded potential
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