Physics – Mathematical Physics
Scientific paper
2011-11-17
Physics
Mathematical Physics
Scientific paper
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.
Campos Hugo M.
Kravchenko Vladislav V.
Mendez Luis M.
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