 The eigenstates of the number operator are the basis of tensor product states
formula_103 where the states formula_104 of the field are the those with a definite number formula_2 of photons.The number operator formula_106 counts the "total" number formula_2 of quanta in the atom-field system.In this basis of eigenstates of formula_106 (total number states), the Hamiltonian takes on a block diagonal structure