The Schrödinger Process

Sergey A. Rashkovskiy

It is shown that the Schrödinger equation can be written in the form of the diffusion equation for classical particles moving in a continuous space. A class of classical random processes described by the Schrödinger equation is considered. It is shown that such classical random processes can be used as a tool for the numerical solution of the Schrödinger equation.

Piotr Garbaczewski, Robert Olkiewicz

Ijaz Durrani

Leon Bess

A diffusion process has been formulated to have a mass conservation equation and a momentum conservation equation that together are equivalent to the Schrödinger equation of quantum mechanics. It is suggested that this diffusion process be used as a physical model to help describe the microphysical processes that underlie the Schrodinger equation.

Masao Nagasawa

Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.