S. Graffi, A. Martinez, M.Pulvirenti
Mean-Field Approximation of Quantum Systems and Classical Limit
(34K, AMS-tex)
ABSTRACT. We prove that, for a smooth two-body potentials, the quantum mean-field approximation to the nonlinear Schr\"odinger equation of the Hartree type is stable at the classical limit $h \to 0$, yielding the classical Vlasov equation.