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Quasi-exact solvability in a general polynomial setting

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dc.contributor.authorGómez-Ullate Otaiza, David
dc.contributor.authorKamran, Niky
dc.contributor.authorMilson, Robert
dc.date.accessioned2023-06-20T10:55:08Z
dc.date.available2023-06-20T10:55:08Z
dc.date.issued2007-10
dc.description© IOP Publishing. The research of DGU is supported in part by the Ramón y Cajal program of the Ministerio de Ciencia y Tecnología and by the DGI under grants FIS2005-00752 and MTM2006-00478. The research of NK and RM is supported in part by the NSERC grants RGPIN 105490-2004 and RGPIN-228057-2004, respectively
dc.description.abstractOur goal in this paper is to extend the theory of quasi-exactly solvable Schrodinger operators beyond the Lie-algebraic class. Let P-n be the space of nth degree polynomials in one variable. We first analyze exceptional polynomial subspaces M subset of P-n, which are those proper subspaces of Pn invariant under second-order differential operators which do not preserve Pn. We characterize the only possible exceptional subspaces of codimension one and we describe the space of second-order differential operators that leave these subspaces invariant. We then use equivalence under changes of variable and gauge transformations to achieve a complete classification of these new, non-Lie algebraic Schrodinger operators. As an example, we discuss a finite gap elliptic potential which does not belong to the Treibich-Verdier class.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipRamón y Cajal program of the Ministerio de Ciencia y Tecnología
dc.description.sponsorshipDGI
dc.description.sponsorshipNSERC
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/30841
dc.identifier.doi10.1088/0266-5611/23/5/008
dc.identifier.issn0266-5611
dc.identifier.officialurlhttp://dx.doi.org/10.1088/0266-5611/23/5/008
dc.identifier.relatedurlhttp://iopscience.iop.org
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0610065
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51449
dc.issue.number5
dc.journal.titleInverse problems
dc.language.isoeng
dc.page.final1942
dc.page.initial1915
dc.publisherIOP Publishing
dc.relation.projectIDFIS2005-00752
dc.relation.projectIDMTM2006-00478
dc.relation.projectIDRGPIN 105490-2004
dc.relation.projectIDRGPIN-228057-2004
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordSolvable schrodinger-operators
dc.subject.keywordTangential covers
dc.subject.keywordCalogero
dc.subject.keywordPotentials
dc.subject.keywordMonomials
dc.subject.keywordEquations
dc.subject.keywordAlgebras
dc.subject.keywordSpaces
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleQuasi-exact solvability in a general polynomial setting
dc.typejournal article
dc.volume.number23
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