Classical and Quantum Superintegrability of Stäckel Systems
In this paper we discuss maximal superintegrability of both classical and quantum Stäckel systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stäckel transform to preserve maximal sup...
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| Datum: | 2017 |
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| Sprache: | English |
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Інститут математики НАН України
2017
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148607 |
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| Zitieren: | Classical and Quantum Superintegrability of Stäckel Systems / M. Błaszak, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
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irk-123456789-1486072019-02-19T01:24:28Z Classical and Quantum Superintegrability of Stäckel Systems Błaszak, M. Marciniak, K. In this paper we discuss maximal superintegrability of both classical and quantum Stäckel systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stäckel transform to preserve maximal superintegrability and we apply this condition to our class of Stäckel systems, which yields new maximally superintegrable systems as conformal deformations of the original systems. Further, we demonstrate how to perform the procedure of minimal quantization to considered systems in order to produce quantum superintegrable and quantum separable systems. 2017 Article Classical and Quantum Superintegrability of Stäckel Systems / M. Błaszak, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70H06; 70H20; 81S05; 53B20 DOI:10.3842/SIGMA.2017.008 http://dspace.nbuv.gov.ua/handle/123456789/148607 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In this paper we discuss maximal superintegrability of both classical and quantum Stäckel systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stäckel transform to preserve maximal superintegrability and we apply this condition to our class of Stäckel systems, which yields new maximally superintegrable systems as conformal deformations of the original systems. Further, we demonstrate how to perform the procedure of minimal quantization to considered systems in order to produce quantum superintegrable and quantum separable systems. |
| format |
Article |
| author |
Błaszak, M. Marciniak, K. |
| spellingShingle |
Błaszak, M. Marciniak, K. Classical and Quantum Superintegrability of Stäckel Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Błaszak, M. Marciniak, K. |
| author_sort |
Błaszak, M. |
| title |
Classical and Quantum Superintegrability of Stäckel Systems |
| title_short |
Classical and Quantum Superintegrability of Stäckel Systems |
| title_full |
Classical and Quantum Superintegrability of Stäckel Systems |
| title_fullStr |
Classical and Quantum Superintegrability of Stäckel Systems |
| title_full_unstemmed |
Classical and Quantum Superintegrability of Stäckel Systems |
| title_sort |
classical and quantum superintegrability of stäckel systems |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148607 |
| citation_txt |
Classical and Quantum Superintegrability of Stäckel Systems / M. Błaszak, // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT błaszakm classicalandquantumsuperintegrabilityofstackelsystems AT marciniakk classicalandquantumsuperintegrabilityofstackelsystems |
| first_indexed |
2025-07-12T18:57:44Z |
| last_indexed |
2025-07-12T18:57:44Z |
| _version_ |
1837468659291783168 |