  We study integrable lattice regularizations of the sine-Gordon model with the
help of the separation of variables method of Sklyanin and the Baxter
Q-operators. This leads us to the complete characterization of the spectrum
(eigenvalues and eigenstates), in terms of the solutions to the Bethe ansatz
equations. The completeness of the set of states that can be constructed from
the solutions to the Bethe ansatz equations is proven by our approach.
