  The first step in the counting operator analysis of the spectrum of any model
Hamiltonian H is the choice of a Hermitean operator M in such a way that the
third commutator with H is proportional to the first commutator. Next one
calculates operators R and R^\dagger which share some of the properties of
creation and annihilation operators, and such that $M$ becomes a counting
operator. The spectrum of H is then decomposed into multiplets, not determined
by the symmetries of H, but by those of a reference Hamiltonian H_ref, which is
defined by H_ref=H-R-R^\dagger, and which commutes with M. Finally, we
introduce the notion of stable eigenstates. It is shown that under rather weak
conditions one stable eigenstate can be used to construct another one.
