With the development of the solid theories and experimental technology

more and more scholars at home and abroad are conducting research on the properties of the magnetopolaron in crystals

there are already many contributions in this field.Peeters

et al

.studied the properties of the magnetopolaron using Feynman’s path integral method.Wei and her co-workers discussed the properties of an interface magnetopolaron using Green-function method.Zorkani

et al

.calculated the ground state energy of bound magnetopolaron using the variational method.Larsen studied the properties of the two-dimensional polaron using an original operator method.Xiao

et al

.discussed the properties of the surface polaron using a linear-combination operator method.Matsura and Lepine studied the problems of polaron which contains many LO phonon branches in polyatomic crystals.Xiao and Hu and other co-workers investgated the many properties of the surface polaron and bulk polaron in polyatomic crystals.Recently Wang and Xiao discussed the excitation state energy of polaron in polyatomic crystals for the first time.The first excitation energy and the mean number of the weak-coupling magnetopolarons in the polyatomic semi-infinite polar crystals were studied by using a linear-combination operator and unitary transformation methods.The results showed that when the electron is approaching infinitely to the surface of crystals

the ground state energy of the magnetopolaron is only the Landau ground state energy

the first excitation energy of the magnetopolaron is twice the Landau ground state energy

and the mean number of phonon is equal to the number of LO phonons and that of SO phonons that each one has coupling with the electron.When the electron is situated in the depth of crystals

the ground state energy of the magnetopolaron is equal to the Landau ground state energy and the energy of LO phonons and SO phonons that each one has coupling with the electron

the first excitation energy of the magnetopolaron is also twice the Landau ground state energy

and the mean number of phonon is equal to the phonon-number of LO phonons concerning depth and that of LO phonons that each one has coupling with the electron

but it is not related to the each branch of SO phonon.