2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185768We 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.LaTeX 2e with amstex package, 36 pagesExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryNew Algebraic Quantum Many-body Problemstext