First-order Darboux transformations for Dirac equations with arbitrary diagonal potential matrix in two dimensions
Department of Mathematics and Actuarial Science, and Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA
Accepted: 26 July 2021
Published online: 31 July 2021
We establish first-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The potential is allowed to depend arbitrarily on both variables. The systems we consider here include the scenario of a position-dependent mass as well as the massless case. Our Darboux transformations are more general than their existing counterparts (Pozdeeva and Schulze-Halberg in J Math Phys 51:113501, 2010).
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021