A potential harmonic method for the three-body Coulomb problem

A potential harmonic method that is suitable for the three-body coulomb systems is presented. This method is applied to solve the three-body Schroedinger equations for He and e(+)e(-)e(+) directly, and the calculations yield very good results for the energy. For example, we obtain a ground-state energy of -0.26181 hartrees for e(+)e(-)e(+), and -2.90300 hartrees for He with finite nuclear mass, in good agreement with the exact values of -0.26200 hartrees and -2.90330 hartrees. Compared with the full-set calculations, the errors in the total energy for ground and excited states of e(+)e(-)e(+) are very small, around -0.0001 hartrees. We conclude that the present method is one of the best PH methods for the three-body coulomb problem.