  We study the many body Schr\"odinger evolution of weakly coupled fermions
interacting through a Coulomb potential. We are interested in a joint mean
field and semiclassical scaling, that emerges naturally for initially confined
particles. For initial data describing approximate Slater determinants, we
prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our
result holds under a condition on the solution of the Hartree-Fock equation,
that we can only show in a very special situation (translation invariant data,
whose Hartree-Fock evolution is trivial), but that we expect to hold more
generally.
