Ensemble Interpretation of Quantum Mechanics and the Two-Slit Experiment

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

“…This formulation incorporates the movement at a given spatial x coordinate as dependent on nearby spatial x coordinates. Such models have been developed in [1] and [10]. The NLAD model supports the ensemble interpretation of quantum mechanics, which maintains that mathematical description of particle behavior should correspond to communal particle behavior, rather than to individual particle behavior [3].…”

“…Schrödinger equation with step function initial data. In [10] an example for the Schrödinger equation applied to the two-slit experiment was given with initial data consisting of two rectangular step functions, symmetric about the origin of the x-axis. In this example, the centers of the two rectangular strips are taken as s = ±1, which can be applied generally by scaling the spatial variable x.…”

“…In the NLAD model in [10], the nonlocal advection term represents directed particle movement due to the influence of nearby particles, and the diffusion term represents variability of particle movement due to stochastic variation. The nonlocal advection term involves an integral corresponding to the slit separation widths s in the ±x-directions.…”

“…The nonlocal advection term involves an integral corresponding to the slit separation widths s in the ±x-directions. In [10], the NLAD equation analyzed is the following:…”

“…In previous work we have investigated mathematical models for the two-slit experiment [9,10]: the Schrödinger equation model (SE) and the nonlocal advection diffusion equation model (NLAD). In this work we extend these investigations to account for higher levels in the fringe patterns images in the experiment.…”