An exact solution of the relativistic Klein-Gordon wave equation (Q1177582)

The authors consider the exact solutions of the relativistic Klein-Gordon equation in electromagnetic fields with a two component vector potential describing the superposition of a stationary magnetic field and the parallel to it proceeding electromagnetic waves. The proposed method uses a unitary representation admitting to lead the given equation to the heat equation with prescribed initial conditions (Cauchy problem). The established Cauchy problem is solved in Cartesian and cylinder coordinates. Concrete examples are given.