Exact coupled set of ordinary differential equations for states of spherical symmetry of a three- body bound-state system

The kinetic-energy operator derived by De Celles and Darling with center-of-mass motion separated is used to derive an orthonormal set of functions for the spherically symmetric states of a three-body bound-state system of arbitrary masses and charges. This approach allows the calculation of the energy $E$ to be reduced to the solution of a coupled system of differential equations in one variable.