On geometro dynamics in atomic stationary states

Abstract

[EN] In a previous paper (G. Gomez Blanch et al, 2018) we defined, in the frame of a geometro-dynamic approach, a metric corresponding to a Lorentzian spacetime where the electron stationary trajectories in a hydrogenoid atom, derived from the de Broglie-Bohm model, are geodesics. In this paper we want to complete this purpose: we will determine the remaining relevant geometrical elements of such an 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 geometrodynamic approaches. Furthermore, we will derive a more general relationship between the Lorentzian metric tensor and the wave function for general monoelectronic stationary states. In our approach, the electron description by the wave function Psi in the Euclidean space and time is shown equivalent to the description by a metric tensor in a Lorentzian manifold. The particle acquires a determining role over the wave function, in a similar manner as the wave function determines the movement of the particle. This dialectic approach overcomes the de Broglie-Bohm approach. And furthermore, a non local element (the quantum potential) is introduced in the model, and incorporated in the geometrodynamic description by the metric tensor.