Discretizing the one-dimensional Dirac equation

Department of Applied Physics, University of Twente 7500 AE Enschede, The Netherlands

Received: 10 November 1998
Accepted: 27 January 1999

Abstract

We suggest a discretization of the Dirac equation based on time symmetry. This iterative scheme is correct to second order in ε, the lattice distance in time, and can therefore be considered as an improvement to the master equation suggested implicitly by Gaveau et al. (Phys. Rev. Lett. 53 1984 419), which generates the Feynman checkerboard propagator. Due to time symmetry this new scheme automatically conserves probability density.