The aforementioned trajectory-based reformulation can be derived either from the stationary or from the time-dependent Schrödinger equation, resulting in differing properties for the trajectories and numerical considerations. In a previous work, some of the authors applied the stationary formulation to the study of quantum scattering processes on a chemical abstraction reaction model as well as in an adiabatic quantum capture model of cold and ultra-cold chemistry, in both cases within the Born-Oppenheimer (adiabatic) approximation. In such contexts, the numerical propagation is extremely stable, essentially because the trajectories are solutions of an ordinary differential equation (ODE).