Mean field dynamics of fermions and the time-dependent Hartree-Fock equation

The time-dependent Hartree-Fock equations are derived from the N-body linear Schrödinger equation with mean-field scaling in the limit N → ∞ and for initial data that are like Slater determinants. Only the case of bounded, symmetric interaction potentials is treated in this work. We prove that, as N →∞, the first partial trace of the N-body density operator approaches the solution of the time-dependent Hartree-Fock equations (in operator form) in the trace norm