Electron propagator solution for an inhomogeneous magnetic field in the momentum space representation

Abstract

The relativistic quantum mechanics of the electron in an inhomogeneous magnetic field problem is solved exactly in terms of the momentum space path integral formalism. We adopt the space–time transformation methods, which are [Formula: see text]-point discretization dependent, to evaluate quantum corrections. The propagator is calculated, the energy eigenvalues and their associated curves are illustrated. The limit case is then deduced for a small parameter.