Asymptotic eigenfunctions for a class of difference operators
- We analyze a general class of difference operators H(epsilon) = T(epsilon) + V(epsilon) on l(2)((epsilon Z)(d)), where V(epsilon) is a one-well potential and epsilon is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H(epsilon). These are obtained from eigenfunctions or quasimodes for the operator H(epsilon), acting on L(2)(R(d)), via restriction to the lattice (epsilon Z)(d).
| Author details: | Markus KleinGND, Elke RosenbergerORCiD |
|---|---|
| DOI: | https://doi.org/10.3233/ASY-2010-1025 |
| ISSN: | 0921-7134 |
| Title of parent work (English): | Asymptotic analysis |
| Publisher: | IOS Press |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2011 |
| Publication year: | 2011 |
| Release date: | 2017/03/26 |
| Tag: | WKB-expansion; difference operator; quasimodes; tunneling |
| Volume: | 73 |
| Issue: | 1-2 |
| Number of pages: | 36 |
| First page: | 1 |
| Last Page: | 36 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
