Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation

The eigenvalue problem for a quantum model of electron-phonon interaction on a discrete Iattice is treated as an equation with operator coefficients, and Maslov's operator method is used to construct series of asymptotic eigenfunctions and eigenvalues with respect to the small parameter corresponding to the interaction of the light and heavy particles.