Beyond Volkov: Solving the Second-Order Klein-Gordon Equation

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.