Asymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation

dc.creatorElton, Daniel M.
dc.date2003-12-04
dc.date.accessioned2026-07-07T05:03:34Z
dc.date.available2026-07-07T05:03:34Z
dc.descriptionWe consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic function for example). It is shown that the eigenvalues of H+V have asymptotics of the form λ_n(H+V)=λ_n(H)+W(\sqrt n)n^{-1/4}+O(n^{-1/2}\ln(n)) as n\to+\infty, where W is a quasi-periodic function which can be defined explicitly in terms of V.
dc.description18 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0312110
dc.identifierhttp://arxiv.org/abs/math/0312110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69472
dc.subjectSpectral Theory
dc.subjectClassical Analysis and ODEs
dc.subject34L20, 34L40 (Primary) 34E10, 81Q10 (Secondary)
dc.titleAsymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation
dc.typetext

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