Bound states in soft quantum layers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912217922797568 |
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| author | Krejcirik, David Kriz, Jan |
| author_facet | Krejcirik, David Kriz, Jan |
| contents | We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus in the Euclidean space. If the surface is asymptotically planar in a suitable sense, we give an estimate on the location of the essential spectrum of the Schroedinger operator. Moreover, if the surface coincides up to a compact subset with a surface of revolution with strictly positive total Gauss curvature, it is shown that the Schroedinger operator possesses an infinite number of discrete eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04919 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bound states in soft quantum layers Krejcirik, David Kriz, Jan Mathematical Physics Differential Geometry Spectral Theory Quantum Physics We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus in the Euclidean space. If the surface is asymptotically planar in a suitable sense, we give an estimate on the location of the essential spectrum of the Schroedinger operator. Moreover, if the surface coincides up to a compact subset with a surface of revolution with strictly positive total Gauss curvature, it is shown that the Schroedinger operator possesses an infinite number of discrete eigenvalues. |
| title | Bound states in soft quantum layers |
| topic | Mathematical Physics Differential Geometry Spectral Theory Quantum Physics |
| url | https://arxiv.org/abs/2205.04919 |