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Infinite families of superintegrable systems separable in subgroup coordinates

Authors
  • Lévesque, Daniel
  • Post, Sarah
  • Winternitz, Pavel
Type
Preprint
Publication Date
Jul 30, 2012
Submission Date
Jul 30, 2012
Identifiers
DOI: 10.1088/1751-8113/45/46/465204
Source
arXiv
License
Yellow
External links

Abstract

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.

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