Nonresonant quantum dynamics of a relativistic electron in counterpropagating laser beams

We investigate the quantum dynamics of an ultrarelativistic electron interacting with intense counterpropagating laser beams. In contrast to the resonance regime where the stimulated Compton scattering occurs, we focus on a scenario where, in the electron's rest frame, the frequency of the counterpropagating wave significantly exceeds that of the copropagating wave. Leveraging a recently developed approximation for the classical dynamics in this configuration, we solve the Klein-Gordon and Dirac equations using a quasiclassical Wentzel-Kramers-Brillouin (WKB) approach. The resulting spin expectation value reproduces the numerical solution of the Bergmann-Michel-Telegdi (BMT) equation, while the spin-averaged momentum agrees with its classical counterpart, as expected. Crucially, we demonstrate that, under certain conditions, the wave function's sensitivity to the electron's momentum causes the normalized acceleration $\ensuremath{\chi}$ of a quantum wave packet to deviate significantly from the classical value. This finding implies that emission processes cannot be accurately described by classical theory, even in the low-$\ensuremath{\chi}$ regime. The derived wave functions provide a foundation for calculating probabilities of nonlinear QED processes in this common field configuration.