Eur. Phys. J. Plus (2019) 134: 49
https://doi.org/10.1140/epjp/i2019-12460-2

Regular Article

Darboux transformations for the massless Dirac equation with matrix potential: Construction of zero-energy states

Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA

^* e-mail: axgeschu@iun.edu

Received: 20 October 2018
Accepted: 10 December 2018
Published online: 31 January 2019

Abstract

We develop a new method for constructing zero-energy states of the massless Dirac equation with a matrix potential. Our method is based on a Darboux transformation for Schrödinger-type equations featuring quadratically energy-dependent potentials.