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A general formulation of the theory of electron impurity states in a lattice in the extended zone scheme is presented. The dependence of the impurity states on the band structure is discussed, and it is shown that the existence of secondary extrema in the band structure may produce additional bound and resonant states. A prescription is given for computing such states and for estimating the probabilities of transitions to them from the ground state; some properties of these transition probabilities are discussed. Solutions of onedimensional models are presented explicitly.

In this paper we establish criteria of instability of the homogeneous large polaron gas versus the periodic state. We study, in the framework of the Bogolyubov approach of the equilibrium distribution functions, how this transition depends on the parameters of the polar medium (dielectric parameters, electron-phonon coupling constant, polaron density). The temperature dependence of the transition is analyzed, indicating that the stability of the periodic phase can be achieved in a given range of temperatures, depending on the material and the polaron density. The comparison of the total energies of the periodic and homogeneous phases does confirm that the stability of the periodic phase corresponds to the lowest-energy configuration.