A potential harmonic method that is suitable for the three-body coulom
b systems is presented. This method is applied to solve the three-body
Schroedinger equations for He and e(+)e(-)e(+) directly, and the calc
ulations yield very good results for the energy. For example, we obtai
n 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 gr
ound 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 m
ethods for the three-body coulomb problem.