Abstract

GOMEZ I BLANCH, G.  and  FULLANA I ALFONSO, M.J.. On geometro dynamics in atomic stationary states. Rev. mex. fis. [online]. 2019, vol.65, n.2, pp.148-158.  Epub Apr 17, 2020. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.65.148.

In a previous paper (G.Gómez 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 Ψ 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.

Keywords : de Broglie -Bohm; lorentzial manifold; wave function; metric tensor; scalar curvature; quantum potential; energy moment tensor; numerical methods; geometrodynamics.