Energy States in a Dimerized Chain with an Impurity

The quantum coherent property of excitons (electrons) in a dimerized chain with the interaction of an impurity is studied analytically. The energy spectrum and the wavefunctions for both the extended states and the localized states are obtained explicitly, from which the effects of the impurity and the electron-phonon interaction (which models the dimerized chain) are manifested. The symmetry properties for the energy states in the parameter space and the real space are also given.