Electron-phonon interaction in a quantum well

Within the framework of the continuum model, optical polarization modes of lattice vibrations and a Fr\"ohlich-like Hamiltonian of the interaction between an electron and optical phonons are derived. It is found that there are four branches of interface optical modes besides the usual transverse-optical and longitudinal-optical modes. The frequencies of these modes and coupling functions of an electron with the optical phonons are discussed.