  We study, in the semi-classical approximation, the convergence of the quantum
density and the quantum action, solutions to the Madelung equations, when the
Planck constant h tends to 0. We find two different solutions which depend to
the initial density . In the first case where the initial quantum density is a
classical density rho_0(x), the quantum density and the quantum action converge
to a classical action and a classical density which satisfy the statistical
Hamilton-Jacobi equations. These are the equations of a set of classical
particles whose initial positions are known only by the density rho_0(x). In
the second case where initial density
