The trajectory-based perspective of the exact factorization requires to replace the concept of a quantum nuclear wavefunction with an ensemble of trajectories. Formally, this is done by replacing R, a 3N n -dimensional vector, with N n the number of nuclei of the system, with the symbol R α (t). Here, α = 1, . . . , N tr labels the trajectories, that have to be many in order to reproduce the delocalization of the nuclei in configuration space. The trajectory-based nuclear dynamics can be simply summarized using Hamilton's equations