Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
- In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.
| Author details: | Matthias LudewigORCiDGND, Elke RosenbergerORCiD |
|---|---|
| DOI: | https://doi.org/10.1142/S0129055X20500208 |
| ISSN: | 0129-055X |
| ISSN: | 1793-6659 |
| Title of parent work (English): | Reviews in mathematical physics |
| Publisher: | World Scientific |
| Place of publishing: | Singapore |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/01/06 |
| Publication year: | 2020 |
| Release date: | 2023/03/30 |
| Tag: | Schrödinger operators; Semi-classical analysis; WKB approximation; semi-classical limit |
| Volume: | 32 |
| Issue: | 7 |
| Article number: | 2050020 |
| Number of pages: | 28 |
| Funding institution: | Max Planck Institute for Mathematics in BonnMax Planck Society [SFB 647] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik |
| Peer review: | Referiert |
