On the model Hamiltonian of the theory of superconductivity

The model Hamiltonian of the theory of superconductivity is investigated for an infinite volume and a complete study is made of its spectrum. The grand partition function is determined; the equation of state is found; and the existence of a phase transition from the normal to the superconducting s tare is proved. It is shown that in the limit $V=\infty$ the chain of equations for the Green's functions of the model Hamiltonian has two solutions – the free Green's functions and the Green's functions of the approximating Hamiltonian.