Bruno Apolloni, Diego de Falco
Orbital Angular Momentum in Nelson's Stochastic Mechanics
(2627K, "Postscript")

ABSTRACT.  We provide numerical examples of integer-valued functionals of Nelson's stochastic processes. More precisely, we consider stochastic motion, according to Nelson's form of Newton's second law of dynamics, in a magnetic field having an axis z of cylindrical symmetry and a gradient in the direction of this axis. We show that there are two sets of functionals of the stochastic process having the same law as the component of quantum mechanical angular momentum along z. The functionals of the first set involve the coordinates of the process and correctly model the behaviour of the "needle of the measuring apparatus". The functionals of the second set involve the coordinates in a plane orthogonal to z and strongly suggest the possibility of a stochastic model of the collapse of the "system" toward the state indicated by the "needle".