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 $N$ particles 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 $BC_N$ elliptic Calogero–Sutherland model is found among the quasi-exactly solvable models. For certain values of the paramaters of this model, we can explicitly calculate the ground state and the lowest excitations.