2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75109A 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, Latex2eSpectral TheoryMathematical Physics47E05 (Primary) 34L20text