Quantum motion with trajectories: Beyond the Gaussian beam approximation

A quantum model based on the Euler–Lagrange variational approach is proposed. Similarly to classical transport, our approach maintains the description of particle motion in terms of trajectories in a configuration space. Our method is designed to provide some corrections to the classical motion of nearly localized particles due to quantum phenomena. We describe the spatial localization of the particles by extending the usual ansatz which is at the basis of the Gaussian beam method. We discuss the completeness of our ansatz and the connection of our results with the Bohm trajectories approach. Our method finds application in the simulation of the motion of light nuclei in ab initio calculations.