One-Dimensional Exactly Solvable Model of Polaron
  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. 
Yu.A.Kuperin, B.S.Pavlov, R.V.Romanov and G.E.Rudin