Properties of polyacetylene obtained from Green's functions in the coordinate representation

An electronic Green's function for polyacetylene with a soliton is obtained with the use of the continuum model but in a coordinate representation. This representation eliminates the necessity of imposing any specific boundary conditions for eigenstates of the Hamiltonian. The Green's function is easily used to obtain both the electronic density of states and the spatial charge density for the midgap state as well as the conduction and valence bands. It is further used to find an optical-absorption coefficient that satisfies the optical sum rule for the polymer chain with a single soliton.