We consider the evolution of
N bosons, where
N is large, with two-body interactions of the form
N3βv(Nβ⋅),
0≤β≤1. The parameter
β measures the strength of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [25, 26]. For
0≤β<1/2, we derive an error bound of the form
p(t)/Nα, where
α>0 and
p(t) is a polynomial, which implies a specific rate of convergence as
N→∞.