New algebraic quantum many-body problems



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Gómez-Ullate Otaiza, David and González López, Artemio and Rodríguez González, Miguel Ángel (2000) New algebraic quantum many-body problems. Journal of physics A: Mathematical and general, 33 (41). pp. 7305-7335. ISSN 0305-4470

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We 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.

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©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.

Uncontrolled Keywords:Calogero-sutherland model; Lie-algebras; Hypergeometric-functions; Root systems; Dynamical-systems; One dimension; Operators; Potentials
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31107
Deposited On:29 Jun 2015 14:17
Last Modified:10 Dec 2018 15:10

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