A fourth-order superintegrable system with a rational potential related to Painlevé VI
Ian Marquette, Sarah Post, Lisa Ritter
Source record
Source: Crossref
Published: Nov 18, 2020
DOI: 10.1088/1751-8121/abbf06
Open original source ↗Source abstract
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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.