  We consider the semiclassical limit from the Hartree to the Vlasov equation
with general singular interaction potential including the Coulomb and
gravitational interactions, and we prove explicit bounds in the strong
topologies of Schatten norms. Moreover, in the case of fermions, we provide
estimates on the size of the exchange term in the Hartree-Fock equation and
also obtain a rate of convergence for the semiclassical limit from the
Hartree-Fock to the Vlasov equation in Schatten norms. Our results hold for
general initial data in some Sobolev space and any fixed time interval.
