Gómez-Ullate Otaiza, DavidGonzález López, ArtemioRodríguez González, Miguel Ángel2023-06-202023-06-202000-10-200305-447010.1088/0305-4470/33/41/305https://hdl.handle.net/20.500.14352/59635©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.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.engjournal articlehttp://dx.doi.org/10.1088/0305-4470/33/41/305http://iopscience.iop.orghttp://arxiv.org/abs/nlin/0003005open access51-73Calogero-sutherland modelLie-algebrasHypergeometric-functionsRoot systemsDynamical-systemsOne dimensionOperatorsPotentialsFísica-Modelos matemáticosFísica matemática