Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

Axel Schulze-Halberg; Pinaki Roy

doi:10.1016/j.aop.2021.168534

paper

Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

arXiv:2102.13561 · doi:10.1016/j.aop.2021.168534

Abstract

We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darbouxtransformed Dirac equations for which the zero energy solutions are exactly known.