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Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

J. Math. Phys. 47, 043514 (2006); doi:10.1063/1.2191789

Published 27 April 2006

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E. G. Kalnins
Department of Mathematics and Statistics, University of Waikato, Hamilton, New Zealand

J. M. Kress
School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia

W. Miller, Jr.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems. ©2006 American Institute of Physics
History: Received 14 January 2006; accepted 10 March 2006; published 27 April 2006
Permalink: http://link.aip.org/link/?JMAPAQ/47/043514/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 03.65.Sq
    Semiclassical theories and applications in quantum mechanics
  • 02.30.Uu
    Integral transforms
  • 02.30.Tb
    Operator theory
  • YEAR: 2006

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PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (22)
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