On geometro dynamics in atomic stationary states

Abstract

In a previous paper [G.Gomez Blanch and M.J.Fullana, 2017] we dened, in the frame of a geometro-dynamic approach, a metric corresponding to a lorentzian spacetime were the electron stationary trajectories in an hydrogenoid atom, derived from the de Broglie-Bohm model, are geodesics. In this paper we want to complete this purpose: we will determinate the remaining relevant geometrical elements of that approach and we will calculate the energetic density component of the energy-momentum tensor. We will discuss the meaning of the obtained results and their relationship with other geometro-dynamic approaches.Furthermore, we will derive a more general relationship between the lorentzian metric tensor and the wave function for general stationary states. The electron description by the wave function ψ in the Euclidean space and time is shown equivalent to the description by a metric tensor in an lorentzian manifold. In our approach, the particle acquires a determining role over thewave function, in a similar manner as the wave function determines the movement of the particle. This dialectic approach overcomes the de Broglie-Bohm model. And furthermore, a non local element (the quantum potential) is introduced in the model, that therefore goes beyond the relativistic locality.