Spurious terms in three-body problem

The method of hyperharmonics is applied to construct the splitting of central pair interactions and the Faddeev components of the three-body wave function into physical and spurious terms. The sum of physical terms of the interactions or Faddeev components over all pairs of particles is not equal to zero, while the sums of spurious terms of the interactions and the Faddeev components over all pairs of particles are identical with zero. The existence criterion for spurious terms is proved. It is shown that a sufficient condition of this criterion is equivalent to the conservation law for a quantum number