
the un-perturbed ground state is 1/√L1 ei q|0>(in perturbation method)and trial wavefunction |ψ>=U1U2|0>(in LLP method). In the weak coupling (with perturbation method)and intermediate coupling(with LLP method)cases,the analytic formulas of ground state energy of the polaron are presented. The self-energy of the polaron
. The result indicates that thelongitudinal deformation potential is contributed to form the bound state of electron, but the effect of the cross deformation potential quite the contrary For general polymers,a, (longitudinal coupling constant) >>a1 (cross coupling constant),therefore the stable polaron can be formed in the mixed dimensional model.