Brownian Motion and the Stochastic Theory of Quantum Mechanics

Abstract

The purpose of this lecture is to give the principles of the simplest stochastic mechanics in configuration space. The work simplest will be explained later; configuration space is the space of the position coordinates of the particles and stochastic mechanics is defined as follows: We call stochastic mechanics to any dynamical theory in which the equations of motion are not fully known. The partial ignorance about the equations of motion is taken into account by introducing stochastic parameters in it. The typical example of stochastic mechanics is the theory of Brownian motion. We distinguish stochastic from statistical mechanics by defining statistical mechanics as a theory in which the differential equations of motion are in principle known even though the initial conditions are not completely specified.