Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-06-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.064 |
| _version_ | 1818884792021680128 |
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| author | Alexander A. Andrianov Andrey V. Sokolov |
| author_facet | Alexander A. Andrianov Andrey V. Sokolov |
| author_sort | Alexander A. Andrianov |
| collection | DOAJ |
| description | When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples. |
| first_indexed | 2024-12-19T15:55:10Z |
| format | Article |
| id | doaj.art-5c88c23fbcf14925bb7f856bd169c844 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-19T15:55:10Z |
| publishDate | 2009-06-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-5c88c23fbcf14925bb7f856bd169c8442022-12-21T20:15:07ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-06-015064Hidden Symmetry from Supersymmetry in One-Dimensional Quantum MechanicsAlexander A. AndrianovAndrey V. SokolovWhen several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.http://dx.doi.org/10.3842/SIGMA.2009.064supersymmetric quantum mechanicsperiodic potentialshidden symmetry |
| spellingShingle | Alexander A. Andrianov Andrey V. Sokolov Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics Symmetry, Integrability and Geometry: Methods and Applications supersymmetric quantum mechanics periodic potentials hidden symmetry |
| title | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_full | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_fullStr | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_full_unstemmed | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_short | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_sort | hidden symmetry from supersymmetry in one dimensional quantum mechanics |
| topic | supersymmetric quantum mechanics periodic potentials hidden symmetry |
| url | http://dx.doi.org/10.3842/SIGMA.2009.064 |
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