  We review some recent results on the norm approximation to the Schr\"odinger
dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction
potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$ with $0\le \beta<1/2$,
and show that in the large $N$ limit, the fluctuations around the condensate
can be effectively described using Bogoliubov approximation.
