For the low-speed electrons

moving along the chains of quasi-one-dimensional polymers

the polymers can be regarded as continuous media. In this paper

a continuons model of mixer dimension (Wilson 1982)is adopted and the interaction of a one-dimensional electron with three-dimensional phonons via deformation potential is discussed. The Hamiltonian of electron-phonon system is

the un-perturbed ground state is 1/√

L

1

e

i q

|0

>

(in perturbation method)and trial wavefunction |ψ

>

=U

1

U

2

|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

<

img style="vertical-align: middle" alt="" order="0" src="http://www.rhhz.net/qikantupian/fgxb-198502-95-2.gif" /

>

. 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)

>

>

a

1

(cross coupling constant)

therefore the stable polaron can be formed in the mixed dimensional model.