<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00966009v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-22T20:13:21+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">QUANTUM PAINLEVÉ II SOLUTION AND APPROXIMATED ANALYTIC SOLUTION OF THE YUKAWA POTENTIAL</title>
            <author role="aut">
              <persName>
                <forename type="first">Irfan</forename>
                <surname>Mahmood</surname>
              </persName>
              <email type="md5">63110a0cf30ead4639af48ff51df6b1f</email>
              <email type="domain">yahoo.com</email>
              <idno type="idhal" notation="numeric">919815</idno>
              <idno type="halauthorid" notation="string">614843-919815</idno>
              <affiliation ref="#struct-396"/>
              <affiliation ref="#struct-117035"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Irfan</forename>
                <surname>Mahmood</surname>
              </persName>
              <email type="md5">63110a0cf30ead4639af48ff51df6b1f</email>
              <email type="domain">yahoo.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2014-03-26 05:38:37</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2014-03-30 05:43:58</date>
              <date type="whenModified">2024-05-02 11:36:27</date>
              <date type="whenReleased">2014-03-31 11:19:27</date>
              <date type="whenProduced">2014-03-30</date>
              <date type="whenEndEmbargoed">2014-03-30</date>
              <ref type="file" target="https://hal.science/hal-00966009v2/document">
                <date notBefore="2014-03-30"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00966009v2/file/1201_5_0900v1.pdf" id="file-967638-642742">
                <date notBefore="2014-03-30"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="169788">
                <persName>
                  <forename>Irfan</forename>
                  <surname>Mahmood</surname>
                </persName>
                <email type="md5">63110a0cf30ead4639af48ff51df6b1f</email>
                <email type="domain">yahoo.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00966009</idno>
            <idno type="halUri">https://hal.science/hal-00966009</idno>
            <idno type="halBibtex">mahmood:hal-00966009</idno>
            <idno type="halRefHtml">2014</idno>
            <idno type="halRef">2014</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-967638-642742"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-NANTES">Université de Nantes</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-ANGERS">Université d'Angers</idno>
            <idno type="stamp" n="LAREMA" corresp="UNIV-ANGERS">Laboratoire Angevin de Recherche en Mathématiques</idno>
            <idno type="stamp" n="FMPL">Fédération de recherche Mathématiques des Pays de Loire</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">QUANTUM PAINLEVÉ II SOLUTION AND APPROXIMATED ANALYTIC SOLUTION OF THE YUKAWA POTENTIAL</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Irfan</forename>
                    <surname>Mahmood</surname>
                  </persName>
                  <email type="md5">63110a0cf30ead4639af48ff51df6b1f</email>
                  <email type="domain">yahoo.com</email>
                  <idno type="idhal" notation="numeric">919815</idno>
                  <idno type="halauthorid" notation="string">614843-919815</idno>
                  <affiliation ref="#struct-396"/>
                  <affiliation ref="#struct-117035"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="it">Quantum PainlevII equation</term>
                <term xml:lang="it">Riccati equation</term>
                <term xml:lang="it">Yukawa potential</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-mp">Mathematics [math]/Mathematical Physics [math-ph]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, it has been shown that one dimensional non- stationary Schrödinger equation with a speci c choice of potential reduces to the quantum Painlevé II equation and the solution of its Riccati form appears as a dominant term of that potential. Further, this article shows that the square of quantum Painlevé II Riccati solution is equivalent to the centrifugal expression of radial schrödinger potential which reduces to the approximated form of Yukawa potential that can be used to solve the radial Schrödinger equation by applying the Nikiforov-Uvarov method.. Finally, I express the approximated form of Yukawa potential explicitly in terms of qunatume Painlevé II solution.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-396" status="VALID">
          <idno type="IdRef">090959531</idno>
          <idno type="ISNI">0000000100733771</idno>
          <idno type="RNSR">200012173L</idno>
          <idno type="ROR">https://ror.org/036j0y719</idno>
          <idno type="Wikidata">Q51780518</idno>
          <orgName>Laboratoire Angevin de Recherche en Mathématiques</orgName>
          <orgName type="acronym">LAREMA</orgName>
          <date type="start">2000-01-01</date>
          <desc>
            <address>
              <addrLine>Université d'Angers, LAREMA - Faculté des Sciences, 2 Boulevard Lavoisier - 49045 Angers CEDEX 01</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-angers.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR6093" active="#struct-74911" type="direct"/>
            <relation name="UMR6093" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-117035" status="VALID">
          <idno type="ROR">https://ror.org/011maz450</idno>
          <orgName>University of the Punjab</orgName>
          <desc>
            <address>
              <addrLine>P.O. Box No. 54590. Lahore</addrLine>
              <country key="PK"/>
            </address>
            <ref type="url">http://pu.edu.pk/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-74911" status="VALID">
          <idno type="IdRef">026402920</idno>
          <idno type="ISNI">0000000122483363</idno>
          <idno type="ROR">https://ror.org/04yrqp957</idno>
          <orgName>Université d'Angers</orgName>
          <orgName type="acronym">UA</orgName>
          <date type="start">1971-10-25</date>
          <desc>
            <address>
              <addrLine>Université d'Angers - 40 Rue de Rennes, BP 73532 - 49035 Angers CEDEX 01</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-angers.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>