Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation

TL;DR

This paper uses Darboux transformations to generate new exactly solvable two-dimensional massless Dirac equations with potentials derived from the Heun equation, focusing on Lambert-W and inverse exponential types.

Contribution

It introduces a method to construct real-valued, elementary-function potentials for the 2D massless Dirac equation based on Heun-class potentials.

Findings

New exactly solvable Dirac potentials of Lambert-W and inverse exponential types.

Conditions for real-valued transformed potentials.

Potential expressions in elementary functions.

Abstract

We apply the Darboux transformation to construct new exactly-solvable cases of the two-dimensional massless Dirac equation for potential classes of Lambert-W and inverse exponential type. Both of these classes originate from the Heun equation. Conditions are devised for transformed potentials to be real-valued, and to be in terms of elementary functions.