arXiv subjects

Dennis M. Heim

Publications and source records attributed to Dennis M. Heim.

3 recordsLinked to original sources

arXiv2026

From Newton's equations to the Schrödinger equation: domain walls as the quantization condition

Can particles at definite positions in real space, obeying Newton's equations under an ordinary interaction force, have a coarse-grained description that is the Schrödinger equation? We present a medium of companion particles on a line under a force of exactly that kind: each companion pays for the mismatch of the signed inverse gaps to its two neighbors. A binary polarity carried by each companion makes stationary states with nodes dynamically stable and supplies the quantization condition. Finite chains relax into the stationary densities of the box and the harmonic oscillator and develop double-slit fringes. In the smooth limit the Schrödinger equation emerges, with $ψ$ carrying two real fields rather than being fundamental.

quant-ph↗

arXiv2022

Revising de Broglie-Bohm trajectories' momentum distribution

Initial momenta of de Broglie-Bohm trajectories generally do not obey quantum mechanical momentum distributions. The solution to this problem presented in the following leads to an extended hydrodynamic interpretation of quantum mechanics. To demonstrate the new formalism, it is applied to the double-slit experiment. From this example follows a proposal for experimental verification of trajectory formulations of quantum mechanics.

quant-ph↗

arXiv2018

Recursive formulation of Madelung continuity equation leads to propagation equation

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.

quant-ph↗