Discretizing the one-dimensional Dirac equation

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1999 EDP Sciences
, , Citation P. P. F. Wessels et al 1999 EPL 46 123 DOI 10.1209/epl/i1999-00234-2

0295-5075/46/2/123

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.

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10.1209/epl/i1999-00234-2