Résumé
Resonances are ubiquitous in a wide range of physical and chemical phenomena. Their impact on quantum scattering processes renders their study as important as it can be puzzling. In this paper, we illustrate the accuracy of a fully quantum, purely trajectory based reformulation of quantum mechanics proposed by one of the authors (Poirier) to acquire insights on shape resonances through direct and accurate computation of the diagonal elements of Smith’s lifetime matrix. This study also generalizes the relationship between the quantum trajectory propagation time and the Eisenbud–Wigner time delay – introduced in our previous publication (Dupuy et al., 2022) for symmetric potentials – to the general case of asymmetric potential profiles. In addition, we show how the complex amplitudes of the scattering matrix can be extracted from left- and right-incident quantum trajectories. Finally, we demonstrate that extended phase space quantum trajectories not only recover -matrix and quantum time quantities, but they also provide their own picture of resonant phenomena, as dynamically distinct events characterized by an integer number of closed orbits in the quantum phase space.