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arXiv · 1207.6976

Infinite families of superintegrable systems separable in subgroup coordinates

Daniel Lévesque·Sarah Post·Pavel Winternitz
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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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Daniel Lévesque, Sarah Post, Pavel Winternitz. 2012-07-30. Infinite families of superintegrable systems separable in subgroup coordinates. https://doi.org/10.1088/1751-8113%2F45%2F46%2F465204

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