High energy asymptotics and trace formulae for the perturbed harmonic oscillator

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A 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.
15 pages, Latex2e

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Spectral Theory, Mathematical Physics, 47E05 (Primary) 34L20

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http://salesiana.dossiersoluciones.com/handle/123456789/75109

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505131
 http://arxiv.org/abs/math/0505131

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arXiv