Monte Carlo generation of Bohmian trajectories
Timothy M. Coffey, Róbert E. Wyatt, William C. Schieve
We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=nδt (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\infty and δt -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.
arXiv:0807.0209•Journal of Physics A Mathematical and Theoretical•Jul 15, 2008•11 citations