Complete families of solutions for the Dirac equation: an application of bicomplex pseudoanalytic function theory and transmutation operators
Abstract
The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables it reduces to a pair of decoupled bicomplex Vekua-type equations [8]. Using the technique developed for complex Vekua equations a system of exact solutions for the bicomplex equation is conctructed under additional conditions, in particular when the electromagnetic potential is absent and the scalar potential is a function of one Cartesian variable. Introducing a transmutation operator relating the involved bicomplex Vekua equation with the Cauchy-Riemann equation we prove the expansion and the Runge approximation theorems corresponding to the constructed family of solutions.
Keywords
Cite
@article{arxiv.1111.4198,
title = {Complete families of solutions for the Dirac equation: an application of bicomplex pseudoanalytic function theory and transmutation operators},
author = {Hugo M. Campos and Vladislav V. Kravchenko and Luis M. Mendez},
journal= {arXiv preprint arXiv:1111.4198},
year = {2011}
}