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Classical and Quantum Superintegrability of Stackel Systems
Adam Mickiewicz University, Poland.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
2017 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 13, 008Article in journal (Refereed) Published
Abstract [en]

In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stackel transform to preserve maximal superintegrability and we apply this condition to our class of Stackel 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.

Place, publisher, year, edition, pages
NATL ACAD SCI UKRAINE, INST MATH , 2017. Vol. 13, 008
Keyword [en]
Hamiltonian systems; classical and quantum superintegrable systems; Stackel systems; Hamilton-Jacobi theory; Stackel transform
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-135404DOI: 10.3842/SIGMA.2017.008ISI: 000393828700001OAI: oai:DiVA.org:liu-135404DiVA: diva2:1081483
Available from: 2017-03-14 Created: 2017-03-14 Last updated: 2017-03-14

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Marciniak, Krzysztof
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