Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids

The quantum trajectory method was recently developed to solve the hydrodyna mic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for fluid elements ("particle s") moving under the influence of the combined force from the potential sur face and the quantum potential. To accurately compute the quantum potential and the quantum force, it is necessary to obtain the derivatives of a func tion given only the values on the unstructured mesh defined by the particle locations. However, in some regions of space-time, the particle mesh shows compression and inflation associated with regions of large and small densi ty, respectively. Inflation is especially severe near nodes in the wave fun ction. In order to circumvent problems associated with highly nonuniform gr ids defined by the particle locations, adaptation of moving grids is introd uced in this study. By changing the representation of the wave function in these local regions (which can be identified by diagnostic tools), propagat ion is possible to much longer times. These grid adaptation techniques are applied to the reflected portion of a wave packet scattering from an Eckart potential. (C) 2000 American Institute of Physics. [S0021-9606(00)01244-7] .