J\"urg Fr\"ohlich, Sandro Graffi, Simon Schwarz
MEAN-FIELD- AND CLASSICAL LIMIT OF MANY-BODY SCHR\"ODINGER DYNAMICS FOR BOSONS
(45K, Latex 2e)

ABSTRACT.  We present a new proof of the convergence of the $N-$particle 
Schr\"odinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a 
restricted class of two-body interactions, we obtain convergence estimates uniform 
in 
$\hbar$, up to an exponentially small remainder. For $\hbar = 0$, the 
classical dynamics in the mean-field limit is given by the Vlasov equation.