A Special Method for Solving the Dirac Equations

Abstract

Exact solutions to the Dirac equations for an electron in an external field of an arbitrary plane wave are obtained by transforming plane wave solutions for a free electron by variable Lorentz matrices. These matrices are those which occur in the discussion of the classical orbits. An example shows that this method, which applies classically, may fail for the Dirac equations when the external field is a constant one.