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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPogosyan, G.S.
dc.date.accessioned2011-08-29T03:02:11Z
dc.date.available2011-08-29T03:02:11Z
dc.date.issued2011
dc.identifier.citationKalnins, E.G., Miller, W., Jr. & Pogosyan, G.S. (2011). Superintegrability and higher-order constants for classical and quantum systems. Physics and Atomic Nuclei, 74(6), 914-918.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/5637
dc.description.abstractWe extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are higher order differential operators than two. Indeed they conjectured that for a general class of potentials of this type, quantum constants of higher order should exist. We give credence to this conjecture by showing that for an even more general class of potentials in classicalmechanics, there are higher-order constants of the motion as polynomials in the momenta. Thus these systems are all superintegrable.en_NZ
dc.language.isoen
dc.publisherSpringeren_NZ
dc.relation.urihttp://www.springerlink.com/content/j1l3x4xj12230148/en_NZ
dc.subjectmathematicsen_NZ
dc.titleSuperintegrability and higher-order constants for classical and quantum systemsen_NZ
dc.typeJournal Articleen_NZ
dc.identifier.doi10.1134/S1063778811060159en_NZ
dc.relation.isPartOfPhysics of Atomic Nucleien_NZ
pubs.begin-page914en_NZ
pubs.elements-id38348
pubs.end-page918en_NZ
pubs.issue6en_NZ
pubs.volume74en_NZ


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