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Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems

J. Math. Phys. 47, 093501 (2006); doi:10.1063/1.2337849

Published 5 September 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 paper is the conclusion 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. For two-dimensional and for conformally flat three-dimensional spaces with nondegenerate potentials we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension. We also correct an error in an earlier paper in the series (that does not alter the structure results) and we elucidate the distinction between superintegrable systems with bases of functionally linearly independent and functionally linearly dependent symmetries. ©2006 American Institute of Physics
History: Received 18 April 2006; accepted 18 July 2006; published 5 September 2006
Permalink: http://link.aip.org/link/?JMAPAQ/47/093501/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 02.10.De
    Algebraic structures and number theory
  • YEAR: 2006

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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (27)
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