High energy asymptotics and trace formulae for the perturbed harmonic oscillator

2005/05/08 by Alexander Pushnitski, Pushnitski, Alexander, Ian Sorrell +1
Mathematics · Physics and Astronomy · #47E05 (Primary) 34L20 #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34L20 #msc:47E05

paper · pdf · doi:10.48550/arxiv.math/0505131

15 pages, Latex2e

arxiv created 2005/05/08 · openalex publication_date 2005/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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