Spurious terms in the three-body problem

The method of hyperharmonics is used to split the central two-body interactions and the Faddeev components of the wave function in a three-body system into physical and spurious terms. The sum of the physical terms of the interactions or of the Faddeev components for all pairs of particles is nonzero, whereas the sums of spurious terms of both the interactions and the Faddeev components over all pairs of particles vanish identically. We establish a criterion for the existence of spurious terms. We show that a sufficient condition for this criterion is equivalent to the conservation law for a certain quantum number.