https://doi.org/10.1140/epjp/s13360-022-03030-w
Regular Article
Darboux transformations for Dirac equations in polar coordinates with vector potential and position-dependent mass
Department of Mathematics and Actuarial Science, and Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA
Received:
7
February
2022
Accepted:
1
July
2022
Published online:
19
July
2022
We construct two Darboux transformations of arbitrary order for the Dirac equation in cylindrical coordinates. The systems we consider include a vector potential and a position-dependent mass that depend on the radial coordinate only. A reality condition for second-order Darboux transformations is derived, and applications to systems supporting bound states are presented. Our construction is based on a formalism for coupled Korteweg–de Vries systems (Ustinov NV and Leble SB in J Math Phys 34:1421, 1993).
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
