  We derive a formulation of mixed quantum-classical dynamics for describing
electronic carriers interacting with phonons in reciprocal space. For
dispersionless phonons, we start by expressing the real-space classical
coordinates in terms of complex variables. A Fourier series over these
coordinates then yields the reciprocal-space coordinates. Evaluating the
electron-phonon interaction term through Ehrenfest's theorem, we arrive at a
reciprocal-space formalism that is equivalent to mean-field mixed
quantum-classical dynamics in real space. This equivalence is numerically
verified for the Holstein and Peierls models, for which we find the
reciprocal-space Hellmann-Feynman forces to involve momentum derivative
contributions in addition to the position derivative terms commonly seen in
real space. We close by presenting a proof of concept for the inexpensive
modeling of low-momentum carriers interacting with phonons by means of a
truncated basis in reciprocal space, which is not possible within a real space
formulation.
