  We present a general approach for the solution of the three-body problem for
a general interaction, and apply it to the case of the Coulomb interaction.
This approach is exact, simple and fast. It makes use of integral equations
derived from the consideration of the scattering properties of the system. In
particular this makes full use of the solution of the two-body problem, the
interaction appearing only through the corresponding known T-matrix. In the
case of the Coulomb potential we make use of a very convenient expression for
the T-matrix obtained by Schwinger. As a check we apply this approach to the
well-known problem of the Helium atom ground state and obtain a perfect
numerical agreement with the known result for the ground state energy. The wave
function is directly obtained from the corresponding solution. We expect our
method to be in particular quite useful for the trion problem in
semiconductors.
