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.
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September 2006
Research Article|
September 05 2006
Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems Available to Purchase
E. G. Kalnins;
E. G. Kalnins
Department of Mathematics and Statistics,
University of Waikato
, Hamilton, New Zealand
Search for other works by this author on:
J. M. Kress;
J. M. Kress
a)
School of Mathematics, The
University of New South Wales
, Sydney NSW 2052, Australia
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W. Miller, Jr.
W. Miller, Jr.
b)
School of Mathematics,
University of Minnesota
, Minneapolis, Minnesota, 55455
Search for other works by this author on:
E. G. Kalnins
Department of Mathematics and Statistics,
University of Waikato
, Hamilton, New Zealand
J. M. Kress
a)
School of Mathematics, The
University of New South Wales
, Sydney NSW 2052, Australia
W. Miller, Jr.
b)
School of Mathematics,
University of Minnesota
, Minneapolis, Minnesota, 55455a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
J. Math. Phys. 47, 093501 (2006)
Article history
Received:
April 18 2006
Accepted:
July 18 2006
Citation
E. G. Kalnins, J. M. Kress, W. Miller; Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems. J. Math. Phys. 1 September 2006; 47 (9): 093501. https://doi.org/10.1063/1.2337849
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