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Quasi-exact solvability and the direct approach to invariant subspaces

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dc.contributor.authorGómez-Ullate Otaiza, David
dc.contributor.authorKamran, Niky
dc.contributor.authorMilson, Robert
dc.date.accessioned2023-06-20T10:55:32Z
dc.date.available2023-06-20T10:55:32Z
dc.date.issued2005-03-04
dc.description©IOP science. The research of DGU is supported in part by a CRM-ISM Postdoctoral Fellowship and the Spanish Ministry of Education under grant EX2002-0176. The research of NK and RM is supported by the National Science and Engineering Research Council of Canada. DGU would like to thank the Department of Mathematics and Statistics of alhousie University for their warm hospitality.
dc.description.abstractWe propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: we show that the generalized Lame potential possesses four algebraic sectors, and describe a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipSpanish Ministry of Education
dc.description.sponsorshipNational Science and Engineering Research Council of Canada
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/30913
dc.identifier.doi10.1088/0305-38/9/011
dc.identifier.issn0305-4470
dc.identifier.officialurlhttp://dx.doi.org/10.1088/0305-4470/38/9/011
dc.identifier.relatedurlhttp://iopscience.iop.org/
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0401030
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51461
dc.issue.number9
dc.journal.titleJournal of physics A: Mathematical and general
dc.language.isoeng
dc.page.final2019
dc.page.initial2005
dc.publisherIOP science
dc.relation.projectIDCRM-ISM Postdoctoral Fellowship
dc.relation.projectIDEX2002-0176
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordDifferential-operators
dc.subject.keywordLame equation
dc.subject.keywordPotentials
dc.subject.keywordAlgebra
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleQuasi-exact solvability and the direct approach to invariant subspaces
dc.typejournal article
dc.volume.number38
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