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 $\chi$ 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-$\chi$ regime. The derived wave functions provide a foundation for calculating probabilities of nonlinear QED processes in this common field configuration.

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• Dirac equation
• Semiclassical methods