Abstract
The correlations between the hyperspherical harmonic transformations and the generalized Talmi–Moshinsky transformations are studied for the three-body and four-body systems. An optical approach for solving few-body problems through diagonalizing the Hamiltonian of a system in an optimal subset of the basis functions of harmonic oscillators in hyperspherical coordinates is proposed. The evaluations of the interaction matrix elements are achieved with the aid of the transformation properties of hyperspherical harmonics.