Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction

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.