ABSTRACT
This chapter presents the celebrated work of Holstein for the derivation of the Holstein Hamiltonian. The description of the polaron within the framework of the tight-binding model has been given by Holstein. The chapter considers the motion of an electron in a one-dimensional molecular crystal. It examines that the tight-binding model to the one-dimensional molecular crystal system in the same way as is used for a chain of atoms in which electrons are tightly bound to the atoms. The electron wave function may be described by the superposition of the atomic orbitals and the tight-binding model provides a suitable description for the study of the electronic properties of narrow-band systems. Thus within the tight-binding scenario, one would expect the electron band to become narrower due to polaron formation.
