Spectral properties of Schroedinger operators with a strongly attractive delta interaction supported by a surface
| dc.creator | Exner, Pavel | |
| dc.date | 2003-01-15 | |
| dc.date.accessioned | 2026-07-07T04:29:43Z | |
| dc.date.available | 2026-07-07T04:29:43Z | |
| dc.description | We investigate the operator $-Δ-αδ(x-Γ)$ in $L^2(\mathbb{R}^3)$, where $Γ$ is a smooth surface which is either compact or periodic and satisfies suitable regularity requirements. We find an asymptotic expansion for the lower part of the spectrum as $α\to\infty$ which involves a ``two-dimensional'' comparison operator determined by the geometry of the surface $Γ$. In the compact case the asymptotics concerns negative eigenvalues, in the periodic case Floquet eigenvalues. We also give a bandwidth estimate in the case when a periodic $Γ$ decomposes into compact connected components. Finally, we comment on analogous systems of lower dimension and other aspects of the problem. | |
| dc.description | AMSTeX, 12 pages; to appear in Proceedings of the NSF Summer Research Conference (Mt. Holyoke 2002); AMS "Contemporary Mathematics" Series, Providence, R.I., 2003 | |
| dc.identifier | https://arxiv.org/abs/math-ph/0301021 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0301021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57265 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Condensed Matter | |
| dc.subject | Quantum Physics | |
| dc.title | Spectral properties of Schroedinger operators with a strongly attractive delta interaction supported by a surface | |
| dc.type | text |