  We study the time evolution of a system of $N$ spinless fermions in
$\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb
potential. We compare the dynamics given by the solution to Schr{\"o}dinger's
equation with the time-dependent Hartree-Fock approximation, and we give an
estimate for the accuracy of this approximation in terms of the kinetic energy
of the system. This leads, in turn, to bounds in terms of the initial total
energy of the system.
