Diffusion-Schrödinger Quantum Mechanics

Nima Moshayedi

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.

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.

Donald D. Fitts

Mojmír Poprocký

The Schrodinger's equation and the diffusion equation can be written in a similar form. While the Schrodinger's equation is complex, the diffusion equation is real. In this thesis we wish to outline similarities of both equations. We present a way to treat a problem in non-relativistic quantum mechanics as a diffusion process. This shows that under certain circumstances both theories are equivalent. We demonstrate this on a few simple examples.

Daniel R. Bes