New Two-Dimensional Quantum Models with Shape Invariance

TL;DR

This paper constructs new two-dimensional quantum models exhibiting shape invariance, using polynomial SUSY Quantum Mechanics, which are integrable but do not allow standard separation of variables.

Contribution

It introduces novel two-dimensional shape invariant quantum models derived from known one-dimensional potentials within polynomial SUSY Quantum Mechanics.

Findings

Models are integrable with fourth-order symmetry operators.

They are built from known one-dimensional shape invariant potentials.

Models do not permit conventional separation of variables.

Abstract

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional SUSY Quantum Mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.