Models of quadratic quantum algebras and their relation to classical superintegrable systems

Journal Article · Fri May 15 00:00:00 EDT 2009 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778809050081· OSTI ID:21405930

Miller, W; Post, S ^[1]

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1. University of Minnesota, School of Mathematics (United States)

We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.

• OSTI ID: 21405930
• Journal Information: Physics of Atomic Nuclei, Vol. 72, Issue 5; Other Information: DOI: 10.1134/S1063778809050081; Copyright (c) 2009 Pleiades Publishing, Ltd.; ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
INTEGRAL CALCULUS
POISSON EQUATION
POLYNOMIALS
QUANTUM OPERATORS
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS