  Whether monochromatic, pulsed, or even constant and crossed, the field used
to describe the interaction of charged fermions with an intense laser beam is
mainly assumed to be of plane-wave form. We consider a simple extension to
plane-wave fields and consider a scalar particle in a non-lightlike, univariate
and transverse propagating electromagnetic wave. The existence of some known
exact solutions in this case allows us to analyse various proposed
approximations in the literature as well as the plane wave model. The results
also describe some of the quantum dynamics of a scalar particle in a standing
wave background.
