High energy asymptotics and trace formulae for the perturbed harmonic oscillator

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dc.creatorPushnitski, Alexander
dc.creatorSorrell, Ian
dc.date2005-05-08
dc.date.accessioned2026-07-07T05:19:41Z
dc.date.available2026-07-07T05:19:41Z
dc.descriptionA one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $λ_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients of this expansion are expressed in terms of the heat invariants. A sequence of trace formulas is obtained, expressing regularised sums of integer powers of eigenvalues $λ_n$ in terms of the heat invariants.
dc.description15 pages, Latex2e
dc.identifierhttps://arxiv.org/abs/math/0505131
dc.identifierhttp://arxiv.org/abs/math/0505131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75109
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject47E05 (Primary) 34L20
dc.titleHigh energy asymptotics and trace formulae for the perturbed harmonic oscillator
dc.typetext

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