2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95417Consider the operator $ T=-{d^2dx^2}+x^2+q(x)$ in $L^2(\mathbb{R})$, where real functions $q$, $q'$ and $\int_0^xq(s)ds$ are bounded. In particular, $q$ is periodic or almost periodic. The spectrum of $T$ is purely discrete and consists of the simple eigenvalues $\{μ_n\}_{n=0}^\infty$, $μ_n<μ_{n+1}$. We determine their asymptotics $μ_n = (2n+1) + (2π)^{-1}\int_{-π}^πq(\sqrt{2n+1}\sinθ)dθ+ O(n^{-1/3})$.LaTeX, 39 pages, 2 postscript figuresMathematical PhysicsSpectral Theory34L20 (Primary) 47N50 (Secondary)text