Spectral asymptotics of the harmonic oscillator perturbed by bounded potentials
- 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.
| Author details: | Markus KleinGND, Evgeni Korotyaev, A. Pokrovski |
|---|---|
| ISSN: | 1424-0637 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2005 |
| Publication year: | 2005 |
| Release date: | 2017/03/24 |
| Source: | Annales Henri Poincare. - ISSN 1424-0637. - 6 (2005), 4, S. 747 - 789 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
