A real space split operator method for the KleinGordon equation
Abstract
The KleinGordon equation is a Lorentz invariant equation of motion for spinless particles. We propose a real space split operator method for the solution of the timedependent KleinGordon equation with arbitrary electromagnetic fields. Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator K^ in the twocomponent representation of the KleinGordon equation is a nilpotent operator, that is K=0, allows us to implement the split operator method for the KleinGordon equation entirely in real space. Consequently, the split operator method for the KleinGordon equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 2009
 DOI:
 10.1016/j.jcp.2009.09.012
 arXiv:
 arXiv:1012.3911
 Bibcode:
 2009JCoPh.228.9092R
 Keywords:

 02.70.c;
 03.65.Pm;
 02.70.Bf;
 Computational techniques;
 simulations;
 Relativistic wave equations;
 Finitedifference methods;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 Computer Physics Communications, vol. 182, nr. 12, pp. 24542463 (2011)