  A classical approximation to time dependent quantum mechanical scattering in
the M\o{}ller formalism is presented. Numerically, our approach is similar to a
standard Classical-Trajectory-Monte-Carlo calculation. Conceptually, however,
our formulation allows one to release the restriction to stationary initial
distributions. This is achieved by a classical forward-backward propagation
technique. As a first application and for comparison with experiment we present
fully differential cross sections for electron impact ionization of atomic
hydrogen in the Erhardt geometry.
