Recent applications of the quantum trajectory method

The de Broglie-Bohm hydrodynamic representation of quantum mechanics is applied to time-dependent wave packet dynamics. The equations of motion for the elements (quasiparticles) of the fluid are integrated in the Lagrangian (‘go with the flow’) viewpoint and are derived for the probability density, velocity, position, and action functions for a discretized wave packet. The particles are influenced by traditional potential energy functions as well as the quantum potential, Q(x), the curvature of the quantum probability amplitude. A weighted moving least-squares algorithm (WMLS) is implemented to obtain derivative information for the equations of motion for the quantum trajectories. This quantum trajectory method (QTM) is applied to barrier tunneling in one and two dimensions, above barrier reflection on a downhill ramp, and nonadiabatic transitions on coupled electronic potential energy surfaces.