Simplified proof for the rate of convergence towards Hartree dynamics

Abstract

We consider a system of $N$ bosons interacting through a two-body potential with Coulomb-type in a non-relativistic case. It is proved by Li Chen, Ji Oon Lee, and Benjamin Schlein that the difference between the many-body Schr\"odinger evolution in the mean field regime and the nonlinear Hartree dynamics is at most of the order $1/N$, for any fixed time. We give a simplified proof of the previous one without using the regularized potential.