  In this paper, we present a microscopic derivation of the two-dimensional
focusing cubic nonlinear Schr\"odinger equation starting from an interacting
$N$-particle system of Bosons. The interaction potential we consider is given
by $W_\beta(x)=N^{-1+2 \beta}W(N^\beta x)$ for some bounded and compactly
supported $W$. We assume the $N$-particle Hamiltonian fulfills stability of
second kind. The class of initial wave functions is chosen such that the
variance in energy is small. We then prove the convergence of the reduced
density matrix corresponding to the exact time evolution to the projector onto
the solution of the corresponding nonlinear Schr\"odinger equation in either
Sobolev trace norm, if the external potential is in some $L^p$ space, $p \in
]2, \infty]$, or in trace norm, for more general external potentials.
