Special Issue in honor of John W. Neuberger Electron. J. Diff. Eqns., Special Issue 02 (2023), pp. 255--267.

Nonlocal advection diffusion equations and the two-slit experiment in quantum mechanics

Glenn Webb

Abstract:
We analyze a partial differential equation that models the two-slit experiment of quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation has a diffusion term corresponding to the random movement of particles, and a nonlocal advection term corresponding to the movement of particles in the transverse direction perpendicular to their forward movement. The model is compared to the Schrodinger equation model of the experiment. The model supports the ensemble interpretation of quantum mechanics.

Published March 27, 2023.
Math Subject Classifications: 35J10, 35Q40.
Key Words: Nonlocal; advection; diffusion; Schrodinger equation; two-slit experiment; ensemble interpretation.
DOI: https://doi.org/10.58997/ejde.sp.02.w1

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Glenn Webb
Mathematics Department
Vanderbilt University
Nashville, TN 37212, USA
email: glenn.f.webb@vanderbilt.edu

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