Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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dc.contributor.author	Quesne, C.
dc.date.accessioned	2019-02-11T15:30:54Z
dc.date.available	2019-02-11T15:30:54Z
dc.date.issued	2011
dc.identifier.citation	Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 90 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 20C35; 81R05; 81R12
dc.identifier.other	DOI:10.3842/SIGMA.2011.035
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146804
dc.description.abstract	The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing D auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and w(2D)⊕s sp(4D,R) dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D=2.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA