Wavepacket dynamics on arbitrary Lagrangian–Eulerian grids: Application to an Eckart barrier

An adaptive grid approach to a computational study of the scattering of a wavepacket from a repulsive Eckart barrier is described. The grids move in an arbitrary Lagrangian–Eulerian (ALE) framework and a hybrid of the moving path transform of the Schrödinger equation and the hydrodynamic equations are used for the equations of motion. Boundary grid points follow Lagrangian trajectories and interior grid points follow non-Lagrangian paths. For the hydrodynamic equations the interior grid points are equally spaced between the evolving Lagrangian boundaries. For the moving path transform of the Schrödinger equation interior grid distribution is determined by the principle of equidistribution, and by using a grid smoothing technique these grid points trace a path that continuously adapts to reflect the dynamics of the wavepacket. The moving grid technique is robust and allows accurate computations to be obtained with a small number of grid points for wavepacket propagation times exceeding 5 ps.