LAUSR

In this paper, we try to solve the Schrodinger equation in a quasi-exact solvable method for a three-body problem with a special interaction and by adding an anharmonic perturbation term. We consider the interaction and perturbation theory in the Calogero model by the roots of algebra \(A_{2}\) and rewrite the Hamiltonian in terms of Lie algebra \(gl_{3} \) and \(g^{2}\) generators. Indeed, we show that the gauge transformed Hamiltonian has infinite invariant flags with finite-dimension. Finally, we obtain a range of eigenvalues and eigenfunctions corresponding to its corrections by using the algebraic framework of the perturbation theory.