Solution of the Dirac-Coulomb problem on the half-line with superstrong magnetic field using differential approach

Abstract

We use the iterated Dirac equation to solve for the eigenfunctions and eigenvalues of a Dirac electron subjected to a uniform superstrong magnetic field and a Coulomb potential confined along the magnetic lines of force. It is shown that by choosing the proper gauge the iterated Dirac equation separates into equations familiar from nonrelativistic quantum mechanics.