On the Stochastic Mechanics Foundation of Quantum Mechanics

Among the famous formulations of quantum mechanics, stochastic picture developed since middle last century remains one less known ones. It is possible to describe mechanical systems with kinetic equations motion in configuration space based on conservative diffusion processes. This leads representation physical observables through processes instead self-adjoint operators. The mathematical foundations this approach were laid by Edward Nelson 1966. allows a different perspective phenomena without necessarily using wave-function. article recaps development mechanics focus variational and extremal principles. Furthermore, recent developments optimal control theory, derivation generalized canonical for within are discussed. These so-called Hamilton add another layer formalisms from classical that find their counterpart mechanics.