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

Mean field limit of bosonic systems in partially factorized states and their linear combinations