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      Superintegrability and higher-order constants for classical and quantum systems

      Kalnins, Ernie G.; Miller, W., Jr.; Pogosyan, G.S.
      DOI
       10.1134/S1063778811060159
      Link
       www.springerlink.com
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      Citation
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      Kalnins, 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.
      Permanent Research Commons link: https://hdl.handle.net/10289/5637
      Abstract
      We 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.
      Date
      2011
      Type
      Journal Article
      Publisher
      Springer
      Collections
      • Computing and Mathematical Sciences Papers [1431]
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