Faddeev Approach to the Ground State of Three-Particle Coulomb Systems

Using a one-state approximation in the Faddeev equations, the ground-state energies of several three-particle Coulomb systems are computed and compared with the earlier variational results. The simplicity and general applicability of this method are in contrast with the variational techniques. Our results also give an idea of the accuracy involved in a one-state approximation for the Faddeev kernel. Some major numerical difficulties are illustrated. Complete analytical expressions for the Faddeev kernel in the two-state approximation are given in an appendix.