  The behavior of massive quantum fields in the general plane wave spacetime
and external, non-plane, electromagnetic waves is studied. The asymptotic
conditions, the "in" ("out") states and the cross sections are analysed. It is
observed that, despite of the singularities encountered, the global form of
these states can be obtained: at the singular points the Dirac delta-like
behavior emerges and there is a discrete change of phase of the wave function
after passing through each singular point. The relations between these phase
corrections and local charts are discussed. Some examples of waves of infinite
range (including the circularly polarized ones) are presented for which the
explicit form of solutions can be obtained. All these results concern both the
scalar as well as spin one-half fields; in the latter case the change of the
spin polarization after the general sandwich wave has passed is studied.
