Permutation-symmetric three-body O(6) hyperspherical harmonics in three spatial dimensions

Abstract

We have constructed the three-body permutation symmetric O(6) hyperspherical harmonics which can be used to solve the non-relativistic three-body Schr{\" o}dinger equation in three spatial dimensions. We label the states with eigenvalues of the $U(1)\otimes SO(3{)}_{rot}\subset U(3)\subset O(6)$ chain of algebras and we present the corresponding $K\le 4$ harmonics. Concrete transformation properties of the harmonics are discussed in some detail.

Submitted to the Proceedings of XI International Workshop Lie Theory and Its Applications in Physics, 15 - 21 June 2015, Varna, Bulgaria