O (6) algebraic approach to three bound identical particles in the hyperspherical adiabatic representation

We construct the three-body permutation symmetric O (6) hyperspherical harmonics and use them to solve the non-relativistic three-body Schrodinger equation in three spatial dimensions. We label the states with eigenvalues of the U(1) circle times SO (3)(rot) subset of U(3) subset of O(6) chain of algebras, and we present the K <= 4 harmonics and tables of their matrix elements. That leads to closed algebraic form of low-K energy spectra in the adiabatic approximation for factorizable potentials with square-integrable hyper-angular parts. This includes homogeneous pairwise potentials of degree alpha >= -1. More generally, a simplification is achieved in numerical calculations of non-adiabatic approximations to non-factorizable potentials by using our harmonics. (C) 2016 Elsevier B.V. All rights reserved.