The interesting property of the uncorrelated Hartree product is that, when inserted into Eq. ( ), it yields straightforwardly evolution equations for the marginal amplitudes in the form of TDSEs, where the effects of the TDPES and of the TDVP is averaged over the marginal amplitudes themselves. Namely, inserting the Hartree product form given in Eq. (30) into Eq. ( ), we can derive the evolution equations for the marginal amplitudes, by multiplying by η * (q,t) and integrating over q or by multiplying by χ * (R,t) and integrating over R, thus obtaining