Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse pote...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146798 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential / V. Hussin, I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575206987464704 |
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| author | Hussin, V. Marquette, I. |
| author_facet | Hussin, V. Marquette, I. |
| citation_txt | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential / V. Hussin, I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.
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| first_indexed | 2025-11-26T11:49:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146798 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T11:49:59Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hussin, V. Marquette, I. 2019-02-11T15:23:52Z 2019-02-11T15:23:52Z 2011 Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential / V. Hussin, I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R15; 81R12; 81R50 DOI:10.3842/SIGMA.2011.024 https://nasplib.isofts.kiev.ua/handle/123456789/146798 We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 The research of I. Marquette was supported by a postdoctoral research fellowship from FQRNT of Quebec. V. Hussin acknowledge the support of research grants from NSERC of Canada. Part of this work has been done while V. Hussin visited Northumbria University (as visiting professor and sabbatical leave). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential Article published earlier |
| spellingShingle | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential Hussin, V. Marquette, I. |
| title | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential |
| title_full | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential |
| title_fullStr | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential |
| title_full_unstemmed | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential |
| title_short | Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential |
| title_sort | generalized heisenberg algebras, susyqm and degeneracies: infinite well and morse potential |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146798 |
| work_keys_str_mv | AT hussinv generalizedheisenbergalgebrassusyqmanddegeneraciesinfinitewellandmorsepotential AT marquettei generalizedheisenbergalgebrassusyqmanddegeneraciesinfinitewellandmorsepotential |