{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:21:12Z","timestamp":1759940472047},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Mod. Phys. A"],"published-print":{"date-parts":[[2009,6,20]]},"abstract":"<jats:p>We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, \u03b8 and \u03b7. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.<\/jats:p>","DOI":"10.1142\/s0217751x09046138","type":"journal-article","created":{"date-parts":[[2009,6,22]],"date-time":"2009-06-22T10:22:16Z","timestamp":1245666136000},"page":"2741-2752","source":"Crossref","is-referenced-by-count":24,"title":["NONCOMMUTATIVE QUANTUM MECHANICS AND QUANTUM COSMOLOGY"],"prefix":"10.1142","volume":"24","author":[{"given":"CATARINA","family":"BASTOS","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Instituto Superior T\u00e9cnico, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"given":"ORFEU","family":"BERTOLAMI","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Instituto Superior T\u00e9cnico, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"given":"NUNO COSTA","family":"DIAS","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa, Portugal"}]},{"given":"JO\u00c3O NUNO","family":"PRATA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02506388"},{"key":"rf2","first-page":"032","volume":"9909","author":"Seiberg N.","journal-title":"JHEP"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(03)00059-0"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.72.025010"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0217732305017536"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0217732306019840"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1063\/1.2944996"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.06.073"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.78.023516"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.28.2960"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/8\/7\/005"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.161301"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.70.103512"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.67.025001"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/23\/24\/024"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.141601"},{"key":"rf21","first-page":"013","volume":"0312","author":"Bertolami O.","journal-title":"JHEP"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2009.02.001"},{"key":"rf23","doi-asserted-by":"crossref","DOI":"10.1515\/9781400868568","volume-title":"Homogeneous Relativistic Cosmologies","author":"Ryan M.","year":"1975"}],"container-title":["International Journal of Modern Physics A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217751X09046138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T17:56:46Z","timestamp":1633629406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217751X09046138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,20]]},"references-count":19,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2009,6,20]]}},"alternative-id":["10.1142\/S0217751X09046138"],"URL":"https:\/\/doi.org\/10.1142\/s0217751x09046138","relation":{},"ISSN":["0217-751X","1793-656X"],"issn-type":[{"value":"0217-751X","type":"print"},{"value":"1793-656X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6,20]]}}}