PrPh

Phenomenological Derivation of the Schr¨ odinger Equation

Fernando Ogiba

Published Oct 1, 2011• 4 citations

Abstract

The Schrödinger equation is derived classically assuming that particles present local \nrandom spatial fluctuations compatible with the presence of the zero-point field. With- \nout specifying the forces arising from this permanent matter-field interaction but ex- \nploring its fundamental properties (homogeneity, isotropy and random aspect) to justify \nthe emergence of the continuity equation in one-particle context, these fluctuations are \ndescribed in terms of the probability density. Specifically, the starting point is the as- \nsumption that the local activities, which turn the path followed by the particle totally \nunpredictable, must be associated with an energy proportional to \n@ \nP \n=@ \nt \n. The polar form \nof the wave function, which connects the obtained classical equations with the corre- \nsponding quantum equation, emerges as a by-product of the approach.

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