Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

Details Models of Quadratic Algebras Generated by Superintegrable Systems in 2D Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

2011-04-05

arxiv.org/abs/1104.0734v1

SIGMA 7 (2011), 036, 20 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2011.036

In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system.

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