The exact solution of a three-body problem of Calogero type in one dimension by the SUSY-QM and SGA methods

Abstract

Analytic expressions of the eigenvalues for a non-relativistic Hamiltonian of a three-body problem of the Calogero type can be derived using both the well known method of supersymmetric quantum mechanics SUSY-QM and an independent group theoretic method, namely the spectrum generating algebra SGA. We demonstrate the equivalence of the two methods by developing an algebraic framework through the shape invariance SI property with a change of parameters which involves nonlinear extensions of Lie Algebra.