Solution of three-body Coulomb problems forJ=0

The Schrödinger equation for the S state of the three-body system with arbitrary charge and mass has been solved directly using finite-element analysis. In this analysis, the wave function is approximated piecewise using polynomial interpolation functions. The energy and wave function converge to their exact values as the number of elements is increased. In contrast to standard variational calculations, the error in the expectation value of physical observables is comparable to the error in the energy. Results are reported here for the helium atom and the muonic molecular ion dd${\mathrm{\mu }}^{+}$.