The numerical procedure based on the propagation of quantum trajectories will be henceforth referred to as the "time dependent quantum trajectories" (TDQT) approach. Given that the trajectories are discretized and coupled through the quantum force as evaluated in Eq. ( ), the dynamical PDE ( ) can be thought of as having been replaced by the following set of coupled ODEs in terms of positions {x i } and momenta {p i = M ẋi } for the discrete ensemble of trajectories: