  Using for unperturbed electron and phonon Hamiltonians a representation by
the Jacobi matrices a one-dimensional model of the electron-phonon interaction
is constructed. In frame of the model the polaron and scattering spectral bands
are calculated explicitly as well as the corresponding states. An explicit
formula for the polaron effective mass is derived and the fit of model
parameters is suggested. A connection of the model with the description of
phonon degrees of freedom for quantum wires is discussed.
