RT Journal Article T1 New algebraic quantum many-body problems A1 Gómez-Ullate Otaiza, David A1 González López, Artemio A1 Rodríguez González, Miguel Ángel AB 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. PB IOP Publishing SN 0305-4470 YR 2000 FD 2000-10-20 LK https://hdl.handle.net/20.500.14352/59635 UL https://hdl.handle.net/20.500.14352/59635 LA eng NO ©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. NO DGES DS Docta Complutense RD 10 may 2025