  We study the mean field limit of one-particle reduced density matrices, for a
bosonic system in an initial state with a fixed number of particles, only a
fraction of which occupies the same state, and for linear combinations of such
states. In the mean field limit, the time-evolved reduced density matrix is
proved to converge: in trace norm, towards a rank one projection (on the state
solution of Hartree equation) for a single state; in Hilbert-Schmidt norm
towards a mixed state, combination of projections on different solutions
(corresponding to each initial datum), for states that are a linear
superposition.
