A nonseparable quantum superintegrable system in 2D real Euclidean space

TL;DR

This paper introduces a 2D quantum superintegrable system that is nonseparable, featuring higher-order integrals of motion, and explores its classical counterpart with quantum corrections.

Contribution

It presents the first known nonseparable quantum superintegrable system in 2D Euclidean space with third and fourth order integrals, expanding the class of known superintegrable models.

Findings

Quantum system has no second order integrals of motion.

Quantum and classical systems share similar superintegrability properties.

Quantum corrections are proportional to ^2, affecting the classical-quantum relationship.

Abstract

In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second order integrals of motion but does admit one third and one fourth order integral. We also obtain a classical superintegrable system with the same properties. The quantum system differs from the classical one by corrections proportional to $\hbar^2.$