<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2019000200148</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.65.148</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On geometro dynamics in atomic stationary states]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez i Blanch]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Fullana i Alfonso]]></surname>
<given-names><![CDATA[M.J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universitat Politècnica de València Institut de Matemàtica Multidisciplinària ]]></institution>
<addr-line><![CDATA[València ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2019</year>
</pub-date>
<volume>65</volume>
<numero>2</numero>
<fpage>148</fpage>
<lpage>158</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2019000200148&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2019000200148&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2019000200148&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[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 &#936; 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.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[de Broglie -Bohm]]></kwd>
<kwd lng="en"><![CDATA[lorentzial manifold]]></kwd>
<kwd lng="en"><![CDATA[wave function]]></kwd>
<kwd lng="en"><![CDATA[metric tensor]]></kwd>
<kwd lng="en"><![CDATA[scalar curvature]]></kwd>
<kwd lng="en"><![CDATA[quantum potential]]></kwd>
<kwd lng="en"><![CDATA[energy moment tensor]]></kwd>
<kwd lng="en"><![CDATA[numerical methods]]></kwd>
<kwd lng="en"><![CDATA[geometrodynamics]]></kwd>
</kwd-group>
</article-meta>
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