Spectral asymptotics of harmonic oscillator perturbed by bounded potential

M. Klein, E. Korotyaev, A. Pokrovski

Consider the operator $T=-d^{2}d{x}^2+x^2+q(x)$ in $L^2(\mathbb{R})$, where real functions $q$, $q^{\prime }$ and ${\int }_0^{x}q(s)ds$ are bounded. In particular, $q$ is periodic or almost perio…