Quasi-exactly solvable generalizations of Calogero-Sutherland models

A generalization of the procedures for constructing quasi-exactly solvable models with one degree of freedom to (quasi-)exactly solvable models of N p articles on a line allows deriving many well-known models in the framework of a new approach that does not use root systems. In particular, a BCN elli ptic Calogero-Sutherland model is found among the quasi-exactly solvable mo dels. For certain values of the paramaters of this model, we can explicitly calculate the ground state and the lowest excitations.