<?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>1870-3542</journal-id>
<journal-title><![CDATA[Revista mexicana de física E]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fís. E]]></abbrev-journal-title>
<issn>1870-3542</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1870-35422018000100047</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The one-dimensional harmonic oscillator damped with Caldirola-Kanai Hamiltonian]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Segovia-Chaves]]></surname>
<given-names><![CDATA[Francis]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Surcolombiana Facultad de Ciencias Exactas y Naturales ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>64</volume>
<numero>1</numero>
<fpage>47</fpage>
<lpage>51</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1870-35422018000100047&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1870-35422018000100047&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1870-35422018000100047&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, the solution to the Hamilton-Jacobi equation for the one-dimensional harmonic oscillator damped with the Caldirola-Kanai model is presented. Making use of a canonical transformation, we calculate the Hamilton characteristic function. It was found that the position of the oscillator shows an exponential decay similar to that of the oscillator with damping where the decay is more pronounced when increasing the damping constant  &#947;. It is shown that when  &#947; = 0, the behavior is of an oscillator with simple harmonic motion. However, unlike the damped harmonic oscillator where the linear momentum decays with time, in the case of the oscillator with the Caldirola-Kanai Hamiltonian, the momentum increases as time increases due to an exponential growth of the mass  m ( t ) = m   e  &#947; t.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Hamilton-Jacobi equations]]></kwd>
<kwd lng="en"><![CDATA[Caldirola-Kanai Hamiltonian]]></kwd>
<kwd lng="en"><![CDATA[damped harmonic oscillator]]></kwd>
</kwd-group>
</article-meta>
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