Can Schroedingerist Wavefunction Physics Explain Brownian Motion? III: A One-Dimensional Heavy and Light Particles Model Exhibiting Brownian-Motion-Like Trajectories and Diffusion

TL;DR

This paper presents a one-dimensional wavefunction model with heavy and light particles that demonstrates Brownian-motion-like trajectories and diffusion, incorporating quantum constants into the diffusion process.

Contribution

It introduces a concrete one-dimensional model showing Brownian motion-like behavior, bridging quantum wavefunction theory with classical diffusion phenomena.

Findings

Model exhibits Brownian-Motion-Like trajectories

Diffusion coefficient depends on Planck's constant and light particle mass

Fulfills criteria for diffusive motion with finite perturbation series

Abstract

In two prior papers of this series, it was proposed that a wavefunction model of a heavy particle and a collection of light particles might generate ``Brownian-Motion-Like" trajectories as well as diffusive motion (displacement proportional to the square-root of time) of the heavy particle, but did not exhibit a concrete instance. Here we introduce a one-space-dimensional model which, granted a finite perturbation series, fulfills the criteria for BML trajectories and diffusion. We note that Planck's constant and the molecular mass of light particles make an appearance in the diffusion coefficient, which further differentiates the present theory from the work of Poincar{\'e} and Einstein in the previous century.