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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148607 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862615303808090112 |
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| author | Błaszak, M. Marciniak, K. |
| author_facet | Błaszak, M. Marciniak, K. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-29T13:26:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148607 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T13:26:49Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Błaszak, M. Marciniak, K. 2019-02-18T16:31:01Z 2019-02-18T16:31:01Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148607 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classical and Quantum Superintegrability of Stäckel Systems Article published earlier |
| spellingShingle | Classical and Quantum Superintegrability of Stäckel Systems Błaszak, M. Marciniak, K. |
| title | 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_short | Classical and Quantum Superintegrability of Stäckel Systems |
| title_sort | classical and quantum superintegrability of stäckel systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148607 |
| work_keys_str_mv | AT błaszakm classicalandquantumsuperintegrabilityofstackelsystems AT marciniakk classicalandquantumsuperintegrabilityofstackelsystems |