The Schrödinger equation and the two-slit experiment of quantum mechanics

Webb, Glenn

doi:10.3934/dcdss.2023001

Cited by 2 publications

(2 citation statements)

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“…We have developed a nonlocal advection-diffusion model NLAD for the twoslit experiment of quantum mechanics, in which quantum particles are projected forward, one at a time, through two slits, and detected downstream on a detection surface. Our work here is an extension of the models in [10] and [11], which allowed higher order fringe pattern levels observed in experiments (Figure 2). We compare the NLAD equation model to the Schrödinger equation model SE with initial data consisting of two rectangular steps.…”

Section: Discussionmentioning

confidence: 90%

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

Webb

2023

ejde

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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 directionperpendicular 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. See also https://ejde.math.txstate.edu/special/02/w1/abstr.html

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Section: Discussionmentioning

confidence: 90%

“…In this work we analyze an extension of equation (3.2) to include higher-order fringe pattern levels as seen in Figure (2). The extension of (3.2) to include higher order fringe pattern levels was illustrated in [11] with numerical examples. Equation (3.2) is modified as follows:…”

Section: Nonlocal Advection Diffusion Equation Modelmentioning

confidence: 99%