2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56920We 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 Schrödinger equations.35 pages, latexMathematical PhysicsSpectral Theory35Q55, 45F15, 81Q05, 81V70text