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

Claude Bardos, Francois Golse, Alex D. Gottlieb, Norbert J. Mauser

Published 2002-04-04, updated 2002-11-15Version 4

The time-dependent Hartree-Fock equations are derived from the N-particle Schr\"odinger equation with mean-field scaling in the infinite particle limit, for initial data that are like Slater determinants. Only the case of bounded interaction potentials is treated in this work. We prove that, in the infnite particle limit, the first partial trace of the N-particle density operator approaches the solution of the time-dependent Hartree-Fock equations in the trace norm.