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New algebraic quantum many-body problems

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dc.contributor.authorGómez-Ullate Otaiza, David
dc.contributor.authorGonzález López, Artemio
dc.contributor.authorRodríguez González, Miguel Ángel
dc.date.accessioned2023-06-20T20:07:55Z
dc.date.available2023-06-20T20:07:55Z
dc.date.issued2000-10-20
dc.description©IOP Publishing. It is our pleasure to thank F. Calogero, A. Perelomov, and O. Ragnisco for useful discussions. D. G.-U. is also glad to acknowledge F. Calogero’s warm hospitality at Universitá di Roma (La Sapienza) while this work was in progress. This work is supported in part by DGES Grant PB98-0821.
dc.description.abstractWe develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipDGES
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/31107
dc.identifier.doi10.1088/0305-4470/33/41/305
dc.identifier.issn0305-4470
dc.identifier.officialurlhttp://dx.doi.org/10.1088/0305-4470/33/41/305
dc.identifier.relatedurlhttp://iopscience.iop.org
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0003005
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59635
dc.issue.number41
dc.journal.titleJournal of physics A: Mathematical and general
dc.language.isoeng
dc.page.final7335
dc.page.initial7305
dc.publisherIOP Publishing
dc.relation.projectIDPB98-0821
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordCalogero-sutherland model
dc.subject.keywordLie-algebras
dc.subject.keywordHypergeometric-functions
dc.subject.keywordRoot systems
dc.subject.keywordDynamical-systems
dc.subject.keywordOne dimension
dc.subject.keywordOperators
dc.subject.keywordPotentials
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleNew algebraic quantum many-body problems
dc.typejournal article
dc.volume.number33
dcterms.references[1] Calogero F 1969 J. Math. Phys. 10 2191–7 [2] Calogero F 1971 J. Math. Phys. 12 419–36 [3] Sutherland B 1971 Phys. Rev. A4 2019–21 [4] Olshanetsky M A and Perelomov A M 1981 Phys. Rep. 71 313–400 [5] Olshanetsky M A and Perelomov A M 1983 Phys. Rep. 94 313–404 [6] Rühl W and Turbiner A 1995 Mod. Phys. Lett. 10 2213–21 [7] Brink L, Turbiner A and Wyllard N 1998 J. Math. Phys 39 1285–315 [8] González-López A, Kamran N and Olver P J 1991 J. Phys. A: Math. Gen. 24 3995– 4008 [9] Calogero F 1978 Nuovo Cim. 43B 177–241 [10] Hou X and Shifman M 1999 Int. J. Mod. Phys. A14 2993–3004 [11] Inozemtsev V I and Meshcheryakov D V 1986 Physica Scripta 33 99–104 [12] González-López A, Kamran N and Olver P J 1993 Commun. Math. Phys. 153 117–46 [13] Inozemtsev V I 1984 Physica Scripta 29 518–20 [14] Inozemtsev V I and Meshcheryakov D V 1985 Lett. Math. Phys. 9 13–8 [15] Inozemtsev V I and Meshcheryakov D V 1984 Phys. Lett. 106A 105–8 [16] Minzoni A, Rosenbaum M and Turbiner A 1996 Mod. Phys. Lett. A24 1977–84 [17] Chihara T S 1978 An Introduction to Orthogonal Polynomials (New York: Gordon and Breach) [18] Finkel F, González-López A, and Rodríguez M A 1996 J. Math. Phys. 37 3954–72 [19] Arscott F M 1964 Periodic Differential Equations (Oxford: Pergamon) [20] González-López A, Kamran N and Olver P J 1994 Contemporary Mathematics 160 113–40 [21] Calogero F 1999 J. Math. Phys. 40 4208–26
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relation.isAuthorOfPublicationd781a665-7ef6-44e0-a0da-81f722f1b8ad
relation.isAuthorOfPublication.latestForDiscovery7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc

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