@article{KleinKorotyaevPokrovski2005, author = {Klein, Markus and Korotyaev, Evgeni and Pokrovski, A.}, title = {Spectral asymptotics of the harmonic oscillator perturbed by bounded potentials}, issn = {1424-0637}, year = {2005}, abstract = {Consider the operator T = -d(2)/dx(2) + x(2) + q(x) in L-2 (R), where q is a real function with q' and integral(0)(x) q(s) ds bounded. The spectrum of T is purely discrete and consists of simple eigenvalues. We determine their asymptotics mu(n) = (2n + 1) + (2 pi)(-1) integral(-pi)(pi) q(root 2n+1 sin theta)d theta + O(n(-1/3)) and we extend these results for complex q.}, language = {en} }