An integral representation of solutions to the Klein-Gordon equation (Q1975105)

The authors analyze the method for constructing the analytical solution to the Klein-Gordon equation in the case of a plane-wave electromagnetic field. The problem under study has been reduced to the Cauchy problem for a parabolic equation. The solutions have been constructed in the form of series in the Hermite and Laguerre polynomials, which makes it difficult to calculate quantum-mechanical processes, especially when the field is the superposition of a stationary magnetic field and a plane-wave field. This motivates the construction of solutions to the Cauchy problem in integral form, performed in the present paper.