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]
.