STOCHASTIC MECHANICS AND NONLINEAR SCHRODINGER EQUATION

In this note, a derivation of a certain type of nonlinear Schr5dinger equation based upon stochastic mechanics is presented. A relationship between the definition of stochastic acceleration of a Brownian particle and nonlinear gauge transformations in a wave function description of that particle is obtained. A new parameter is introduced, which scales the nonlinearity. It is indicated how this nonlinear equation is related to the Doebner-Goldin equation and to another approach by Smolin, who introduced a ʹquantum massʹ parameter.