  We consider the dynamics of a large quantum system of $N$ identical bosons in
3D interacting via a two-body potential of the form $N^{3\beta-1}
w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and large $N$, we obtain a norm
approximation to the many-body evolution in the $N$-particle Hilbert space. The
leading order behaviour of the dynamics is determined by Hartree theory while
the second order is given by Bogoliubov theory.
