On the hydrodynamical model of the quantum mechanics

Abstract

A new hydrodynamicla model for the Schrödinger equation is discussed. The new model differs from that of Madelung by the existence of turbulence. It follows directly from the ordinary interpretation of the quantum mechanics, by the introduction of operators for the charge and current densities and the components of the stress tensor in the one particle formalism. The model is developed for any values of the spin. The Madelung fluid corresponds to the mean motion of the special turbulent medium. The quantum potential appears as a combination of a pressure with terms arising from the turbulence. It is shown that the quantization of the motion of the Madelung fluid introduces the right kind of turbulence. The trajectories of the de Broglie-Bohm theory appear as trajectories of the mean motion of the turbulent medium. © 1954 Società Italiana di Fisica.