Recursive formulation of Madelung continuity equation leads to propagation equation

TL;DR

This paper derives a new propagation equation from the Madelung continuity equation using a recursive approach, connecting it to de Broglie-Bohm guidance equations and demonstrating its application in a double-slit experiment scenario.

Contribution

It introduces a recursive formulation of the Madelung continuity equation that results in a novel propagation equation for particle densities, linking fluid dynamics with quantum guidance.

Findings

Derived a recursive propagation equation for Madelung fluid

Connected the propagation equation to de Broglie-Bohm guidance in certain limits

Successfully demonstrated particle propagation in a double-slit experiment scenario

Abstract

We apply a recursive approach to the continuity equation of the Madelung fluid resulting in a propagation equation for particle probability densities. This propagation equation can be used to propagate particle distributions in the presence of a Madelung pressure field. We show that the derived propagation equation goes over into the guidance equation of the de Broglie-Bohm theory in the limit of well located single particles. As an example, we propagate particles that enter the lower slit of a double-slit experiment, while the Madelung fluid enters both slits.