The trajectories can be assimilated to a moving grid: while in the quantum treatment the value of a function f (R,t) can be determined at time t at any point R, in the quantum-classical treatment only the values f (R α (t),t) are accessible. Clearly, for a very large number of trajectories N tr , information is not lost when going from the quantum to the quantum-classical treatment. It is important to note that, in order to evaluate how functions of the type f (R α (t),t) evolve, only total time-derivatives can be computed instead of partial timederivatives.