  We consider a quantum system constituted by $N$ identical particles
interacting by means of a mean-field Hamiltonian. It is well known that, in the
limit $N\to\infty$, the one-particle state obeys to the Hartree equation.
Moreover, propagation of chaos holds. In this paper, we take care of the
$\hbar$ dependence by considering the semiclassical expansion of the
$N$-particle system. We prove that each term of the expansion agrees, in the
limit $N\to\infty$, with the corresponding one associated with the Hartree
equation. We work in the classical phase space by using the Wigner formalism,
which seems to be the most appropriate for the present problem.
