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arXiv · 2006.12639

A fourth-order superintegrable system with a rational potential related to Painleve VI

Ian Marquette·Sarah Post·Lisa Ritter
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Abstract

In this paper, we investigate in detail a superintegrable extension of the singular harmonic oscillator whose wave functions can be expressed in terms of exceptional Jacobi polynomials. We show that this Hamiltonian admits a fourth-order integral of motion and use the classification of such systems to show that the potential gives a rational solution associated with the sixth Painlevé equation. Additionally, we show that the integrals of the motion close to form a cubic algebra and describe briefly deformed oscillator representations of this algebra.

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Ian Marquette, Sarah Post, Lisa Ritter. 2020-09-18. A fourth-order superintegrable system with a rational potential related to Painleve VI. https://doi.org/10.1088/1751-8121%2Fabbf06

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