NONLOCAL ADVECTION DIFFUSION EQUATIONS AND THE TWO-SLIT EXPERIMENT IN QUANTUM MECHANICS

We analyze a partial differential equation that models the twoslit 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.