  The problem of an ultrarelativistic charge in the presence of an atomic and a
plane-wave field is investigated in the quasiclassical regime by including
exactly the effects of both background fields. Starting from the quasiclassical
Green's function obtained in [Phys. Lett. B \textbf{717}, 224 (2012)], the
corresponding in- and out-wave functions are derived in the experimentally
relevant case of the particle initially counterpropagating with respect to the
plane wave. The knowledge of these electron wave functions opens the
possibility of investigating a variety of problems in strong-field QED, where
both the atomic field and the laser field are strong enough to be taken into
account exactly from the beginning in the calculations.
