On Dicke-type hamiltonians with hidden variables

The main theoren about the exactness of the generalized version of the Bogoliubov (Jr.) thermodynamically-equivalent Hamiltonian method for Dicke-type models which include some hidden variables, is proved. Some generalizations are done of earlier investigations according to a Dicke-type model with spatial variation of electromagnetic field and classical Debye vibrations of atoms around their equilibrium positions. They refer to the range of electromagnetic field phase φ and to the violation of the one-mode approximation for vibrations.