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arXiv · 2001.07309

Superintegrability and the dual $-1$ Hahn algebra in superconformal quantum mechanics

Pierre-Antoine Bernard·Julien Gaboriaud·Luc Vinet
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Abstract

A two-dimensional superintegrable system of singular oscillators with internal degrees of freedom is identified and exactly solved. Its symmetry algebra is seen to be the dual $-1$ Hahn algebra which describes the bispectral properties of the polynomials with the same name that are essentially the Clebsch-Gordan coefficients of the superconformal algebra $\mathfrak{osp}(1|2)$. It is also shown how this superintegrable model is obtained under dimensional reduction from a set of uncoupled harmonic oscillators in four dimensions.

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Pierre-Antoine Bernard, Julien Gaboriaud, Luc Vinet. 2020-07-08. Superintegrability and the dual $-1$ Hahn algebra in superconformal quantum mechanics. https://doi.org/10.1016/j.aop.2020.168171

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