Integrable and superintegrable systems with higher order integrals of motion: master function formalism

TL;DR

This paper develops a formalism to construct two-dimensional integrable and superintegrable systems with higher order integrals of motion, linking them to supersymmetric quantum mechanics, and presents specific examples with new higher order integrals.

Contribution

It introduces the master function formalism for constructing superintegrable systems and relates it to existing supersymmetric quantum mechanics frameworks, providing new examples with higher order integrals.

Findings

Constructed two new superintegrable systems with higher order integrals.

Linked the formalism to Mielnik's and Marquette's supersymmetric quantum mechanics.

Demonstrated the applicability of the master function approach to specific cases.

Abstract

In this article, we construct two-dimensional integrable and superintegrable sys- tems in terms of the master function formalism and relate them to Mielnik;s and Marquette;s construction in supersymmetric quantum mechanics. For two diferent cases of the master functions, we obtain two diferent two-dimensional superintegrable systems with higher order integrals of motion.