We analyze in detail below the three models using k 0 = 10 a -1 0 . An overall assessment of the performance of TDQT for k 0 = 10, 15, 20 a -1 0 is provided at the end of the section. In Fig. we present some results for the single avoided crossing model where the initial momentum of the incoming wavepacket is k 0 = 10 a -1 0 . Two snapshots are shown in the figure, at t = 40 fs (left panels) and at t = 120 fs (right panels): in the upper panels the (static) adiabatic, BOPESs are reported in black, together with the TDPES in gold at the two snapshots; in the lower panels the exact nuclear density is shown in black, and is compared to the density reconstructed from TDQT (red) and from TDCT (blue). The evolution of the TDPES manifests the nonadiabatic event by forming a pronounced peak between 0 and 2 a 0 that deforms the Gaussian shape of the nuclear density at t = 40 fs, and also by developing a small bump between 10 a 0 and 15 a 0 that splits the nuclear density into two portions.