Hyperangular Green's functions and the three body problem

A Green's function approach is formulated and used to determine adiabatic hyperspherical potential curves. ~The Green's function is found for the hyperangular part of the non-interacting Schroedinger equation with any number of particles in any number of dimensions. This Green's function is then applied to the three-body problem with regularized, zero-range, pair-wise, s-wave interactions, which determine a quantization condition whose solution yields the adiabatic potential curves for any given total angular momentum and exchange symmetry. ~This method appears to generalize readily to handle multichannel, regularized, zero-range, pair-wise interactions.