A fourth-order superintegrable system with a rational potential related to Painleve VI
Mathematical Physics
2021-10-01 v3 math.MP
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 Painlev\'e 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.
Keywords
Cite
@article{arxiv.2006.12639,
title = {A fourth-order superintegrable system with a rational potential related to Painleve VI},
author = {Ian Marquette and Sarah Post and Lisa Ritter},
journal= {arXiv preprint arXiv:2006.12639},
year = {2021}
}