Explicit Definition of an Observable Event in the Framework of Generalized Madelung Equations

Abstract Contrary to classical mechanics, quantum mechanics does not deal directly with observable events. In order to infer from the knowledge of a quantum state a prediction about an event, it is necessary to call upon the theory of measurement, a complicated system of interpretation of the basic formalism. The Madelung formulation offers seemingly a more direct solution to this problem, since one of its equations of motion assumes a classical form and operates on a local momentum. A critical examination of its limitations leads to the generalization of the Madelung equations. The new local momentum associated to a given state depends on the probability density, the phase of the wave function, and arbitrary quantities. Its spatial average over a finite cell displays the features of the observable momentum. On this ground a model of the observed motion is built up with the help of a minimal set of postulated.