  We consider the time evolution of N bosonic particles interacting via a mean
field Coulomb potential. Suppose the initial state is a product wavefunction.
We show that at any finite time the correlation functions factorize in the
limit $N \to \infty$. Furthermore, the limiting one particle density matrix
satisfies the nonlinear Hartree equation. The key ingredients are the
uniqueness of the BBGKY hierarchy for the correlation functions and a new
apriori estimate for the many-body Schr\"odinger equations.
