  In this paper we analytically study the effects of the lattice discreteness
on the electron band in the SSH model. We propose a modified version of the TLM
model which is derived from the SSH model using a continuum approximation. When
a soliton is induced in the electron-lattice system, the electron scattering
states both at the bottom of the valence band and the top of the conduction
band are attracted to the soliton. This attractive force induces weakly
localized electronic states at the band edges. Using the modified version of
the TLM model, we have succeeded in obtaining analytical solutions of the
weakly localized states and the extended states near the bottom of the valence
band and the top of the conduction band. This band structure does not modify
the order parameters. Our result coincides well with numerical simulation
works.
