Monte Carlo generation of Bohmian trajectories

We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that does not 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 → ∞ and δt → 0. Higher dimensional problems can be solved by this method for separable wavefunctions. Several examples are given, including the two-slit experiment