ABSTRACT
This chapter considers a simple impurity system, namely, a hydrogenic impurity, that is, an electron bound to a hydrogen nucleus, known as the Coulomb impurity. The Green function method can be extended to calculate the energy corrections for the unperturbed first excited states of the Coulomb impurity by employing the appropriate Coulomb Green functions for 2s, 2p states. Quite naturally, the theoretical methods developed for the free polaron problem were extended to investigate the properties of the bound polaron. The chapter presents results with two effective potentials, namely the harmonic oscillator potential and the hydrogenic potential. A variant of the Mukhopadhyay-Mitra method has been used by Devreese, Evrards, Kartheuser, and Brosens to obtain the ground state energy of a bound polaron. The polaron model neglects the short-range potential due to the difference between atomic properties of the donor and the host lattice, the local lattice distortion and the acoustic phonons.
