On geometro dynamics in atomic stationary states
Abstract 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.
| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedad Mexicana de Física
2019
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| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2019000200148 |
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| Summary: | Abstract 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. |
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