High energy asymptotics and trace formulae for the perturbed harmonic oscillator

Details High energy asymptotics and trace formulae for the perturbed harmonic oscillator High energy asymptotics and trace formulae for the perturbed harmonic oscillator

2005-05-08

arxiv.org/abs/math/0505131v1

Mathematics

Spectral Theory

15 pages, Latex2e

Scientific paper

A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, 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 $\lambda_n$ in terms of the heat invariants.

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