Quantum wave packet dynamics with trajectories

The de Broglie-Bohm causual (hydrodynamic) formulation of quantum mechanics is computationally implemented in the Lagrangian (moving with the fluid) view point. The quantum potential and force are accurately evaluated with a moving weighted least squares algorithm. The quantum trajectory method is then applied to barrier tunneling on smooth potential surfaces. Analysis of the tunneling mechanism leads to a novel and accurate approximation: shortly after the wave packet is launched, completely neglect all quantum terms in the dynamical equations for motion along the tunneling coordinate.