Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds
We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in t...
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| Format: | Article |
| Language: | English |
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CTU Central Library
2010-01-01
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| Series: | Acta Polytechnica |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/1271 |
| _version_ | 1818541827530162176 |
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| author | T. Mine |
| author_facet | T. Mine |
| author_sort | T. Mine |
| collection | DOAJ |
| description | We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas. |
| first_indexed | 2024-12-11T22:14:16Z |
| format | Article |
| id | doaj.art-2d6ffef78bb4454a85cb71abb3e27449 |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-12-11T22:14:16Z |
| publishDate | 2010-01-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-2d6ffef78bb4454a85cb71abb3e274492022-12-22T00:48:39ZengCTU Central LibraryActa Polytechnica1210-27091805-23632010-01-015051271Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian ManifoldsT. MineWe consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.https://ojs.cvut.cz/ojs/index.php/ap/article/view/1271Spectral theoryfunctional analysisself-adjointnessAharonov-Bohm effectquantum mechanicsdifferential geometrySchrödinger operator |
| spellingShingle | T. Mine Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds Acta Polytechnica Spectral theory functional analysis self-adjointness Aharonov-Bohm effect quantum mechanics differential geometry Schrödinger operator |
| title | Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds |
| title_full | Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds |
| title_fullStr | Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds |
| title_full_unstemmed | Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds |
| title_short | Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds |
| title_sort | self adjoint extensions of schrodinger operators with magnetic fields on riemannian manifolds |
| topic | Spectral theory functional analysis self-adjointness Aharonov-Bohm effect quantum mechanics differential geometry Schrödinger operator |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/1271 |
| work_keys_str_mv | AT tmine selfadjointextensionsofschrodingeroperatorswithmagneticfieldsonriemannianmanifolds |