Monte Carlo Generation of Bohmian Trajectories

TL;DR

This paper introduces a Monte Carlo method for generating Bohmian trajectories in quantum mechanics that avoids differential equations, using random sampling of quantum probability densities to produce exact solutions in the limit.

Contribution

The paper presents a novel Monte Carlo approach to compute Bohmian trajectories without solving differential equations, applicable to separable wave functions in higher dimensions.

Findings

Accurately reproduces Bohmian trajectories in one dimension.

Applicable to higher dimensions for separable wave functions.

Validated with examples including the two-slit experiment.

Abstract

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=n\delta t (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 \delta t -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.