  By applying variational method, the strong electron-surface optical(SO)
phonon interaction and the weak electron-longitudinal optical (LO) phonon
interaction are studied systematically in present paper. The formula of induced
energy $V_{e-so}$, $V_{e-lo}$ in both the ground and excited states are given.
The numerical results show that as the distance between the electron and the
polar crystal surface increases, the electron-LO phonon interaction energy
increases yet the electron-SO phonon interaction energy decreases. The
numerical results also show that both electron-LO and electron-SO phonon
interaction are enhanced as the magnetic field strength increases.
