Exact solution of the Faddeev equations for the harmonic oscillator ground state

The Faddeev equations in $N$ space dimensions for three identical spinless particles in their ground state interacting via harmonic oscillator, two-body potentials is solved analytically. Unlike the well-known Schrödinger solution, the individual Faddeev amplitudes may be negative and contain a long-range component of arbitrary strength. Upon symmetrizing to obtain the full wave function, this component vanishes and the Schrödinger solution results. Three-dimensional plots of the various wave functions are presented.