Asymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation
| dc.creator | Elton, Daniel M. | |
| dc.date | 2003-12-04 | |
| dc.date.accessioned | 2026-07-07T05:03:34Z | |
| dc.date.available | 2026-07-07T05:03:34Z | |
| dc.description | We consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic function for example). It is shown that the eigenvalues of H+V have asymptotics of the form λ_n(H+V)=λ_n(H)+W(\sqrt n)n^{-1/4}+O(n^{-1/2}\ln(n)) as n\to+\infty, where W is a quasi-periodic function which can be defined explicitly in terms of V. | |
| dc.description | 18 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0312110 | |
| dc.identifier | http://arxiv.org/abs/math/0312110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69472 | |
| dc.subject | Spectral Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34L20, 34L40 (Primary) 34E10, 81Q10 (Secondary) | |
| dc.title | Asymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation | |
| dc.type | text |