  We present an elementary proof based on a direct calculation of the property
of completeness at constant time of the solutions of the Klein-Gordon equation
for a charged particle in a plane wave electromagnetic field. We also review
different forms of the orthogonality and completeness relations previously
presented in the literature and we discuss the possibility to construct the
Feynman propagator for the particle in a plane-wave laser pulse as an expansion
in terms of Volkov solutions. We show that this leads to a rigorous
justification for the expression of the transition amplitude, currently used in
the literature, for a class of laser assisted or laser induced processes.
