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We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef [\u201cA new approach to the \u22c6-genvalue equation,\u201d Lett. Math. Phys.\u200885, 173\u2013183 (2008)].<\/jats:p>","DOI":"10.1063\/1.3436581","type":"journal-article","created":{"date-parts":[[2010,7,2]],"date-time":"2010-07-02T22:56:35Z","timestamp":1278111395000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":20,"title":["A deformation quantization theory for noncommutative quantum mechanics"],"prefix":"10.1063","volume":"51","author":[{"given":"Nuno Costa","family":"Dias","sequence":"first","affiliation":[{"name":"Universidade Lus\u00f3fona de Humanidades e Tecnologias 1 Departamento de Matem\u00e1tica, , Av. Campo Grande, 376, 1749-024 Lisboa, Portugal and Grupo de F\u00edsica Matem\u00e1tica, , Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"},{"name":"Universidade de Lisboa 1 Departamento de Matem\u00e1tica, , Av. Campo Grande, 376, 1749-024 Lisboa, Portugal and Grupo de F\u00edsica Matem\u00e1tica, , Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]},{"given":"Maurice","family":"de Gosson","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien 2 NuHAG Fakult\u00e4t f\u00fcr Mathematik, , Wien 1090, Austria"}]},{"given":"Franz","family":"Luef","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien 2 NuHAG Fakult\u00e4t f\u00fcr Mathematik, , Wien 1090, Austria"},{"name":"UC Berkeley 3 Department of Mathematics, , 847 Evans Hall, Berkeley, California 94720-3840, USA"}]},{"given":"Jo\u00e3o Nuno","family":"Prata","sequence":"additional","affiliation":[{"name":"Universidade Lus\u00f3fona de Humanidades e Tecnologias 1 Departamento de Matem\u00e1tica, , Av. Campo Grande, 376, 1749-024 Lisboa, Portugal and Grupo de F\u00edsica Matem\u00e1tica, , Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"},{"name":"Universidade de Lisboa 1 Departamento de Matem\u00e1tica, , Av. Campo Grande, 376, 1749-024 Lisboa, Portugal and Grupo de F\u00edsica Matem\u00e1tica, , Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2010,7,1]]},"reference":[{"key":"2023072301341130100_c1","doi-asserted-by":"publisher","first-page":"5556","DOI":"10.1016\/j.physleta.2008.06.073","article-title":"Berry phase in the gravitational quantum well and the Seiberg-Witten map","volume":"372","year":"2008","journal-title":"Phys. Lett. A"},{"key":"2023072301341130100_c2","doi-asserted-by":"publisher","first-page":"124038","DOI":"10.1103\/PhysRevD.80.124038","article-title":"Black holes and phase-space noncommutativity","volume":"80","year":"2009","journal-title":"Phys. Rev. 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