Classical and Quantum Superintegrability of Stäckel Systems

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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Date:2017
Main Authors: Błaszak, M., Marciniak, K.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.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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spelling 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
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