Integrable and Superintegrable Systems with Higher Order Integrals of Motion: Master Function Formalism

Abstract

We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik's and Marquette's construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.