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

Journal Article · Fri Sep 15 04:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2337849· OSTI ID:20860897

Kalnins, E G; Kress, J M; Miller, W Jr ^[1]

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1. Department of Mathematics and Statistics, University of Waikato, Hamilton (New Zealand)

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.

• OSTI ID: 20860897
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSIFICATION
MATHEMATICAL SPACE
POTENTIALS
QUANTUM MECHANICS
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS