  The Ehrenfest dynamics, representing a quantum-classical mean-field type
coupling, is a widely used approximation in quantum molecular dynamics. In this
paper, we propose a time-splitting method for an Ehrenfest dynamics, in the
form of a nonlinearly coupled Schr\"odinger-Liouville system. We prove that our
splitting scheme is stable uniformly with respect to the semiclassical
parameter, and, moreover, that it preserves a discrete semiclassical limit.
Thus one can accurately compute physical observables using time steps induced
only by the classical Liouville equation, i.e., independent of the small
semiclassical parameter - in addition to classical mesh sizes for the Liouville
equation. Numerical examples illustrate the validity of our meshing strategy.
