The properties of magnetopolaron in crystals and semiconductors influence on the properties of the crystals and semiconductors very remarkably.With the development of the material science and experimental technology

the properties of magnetopolaron in crystals and semiconductors have been of considerable interest.Many investigators studied the properties of the magnetopolaron by means of various theoretical methods and experimental methods.Wu

et al

.studied the properties of the 2D magnetopolaron using the Feynmann path-integral approach.Wei

et al

.calculated the induced potential

resonance frequency and the self-energy of an interface magnetopolaron using the Green-function method.Lassnig

et al

.discussed the theory of resonant magnetopolaron of 2D electron system in narrow gap semiconductors using the variational method.Madkour

et al

.studied the effect of magnetic field on magnetopolaron states in a polar crystal interface and emphasized the result that the presence of magnetic field leads to a local potential for charge carriers at the interface.Based on Wigner-Brillouin theory

Brancus and Stan investigated the state energy of an anisotropic three-dimensional polaron in a magnetic field.Wollf

et al

.investigated the bound magnetic polarons in semimagnetic semiconductors and the bound magnetic polarons in dilute magnetic semiconductors by the optical experiments.Employing Haga’s perturbation method

Hu

et al

.derived an effective Hamiltonian for the interface magnetopolaron in polar crystals.The properties of surface magnetopolaron in a magnetic field have been further discussed by Xiao and co-workers.Tokuda studied the mean number of phonon of the optical and the piezoelectric polarons by using improved Huybrechts method.However

the mean number of phonon of magnetopolarons in crystals has not been studied so far.In this paper

the properties of magnetopolaron which is a strong-and weak-coupling of optical phonon was discussed by using Tokuda’s improved linear combination operator and the Lagrange multiplier and the variational method.Numerical calculations for RbCI and GaAs crystal

as an example

are performed.The relational of the vibration frequency

the ground state energy and the mean number of optical phonon to magnetic field

B

and Lagrange multiplier

u

are discussed.The result illustrates that the vibration frequency of magnetopolaron will increase with increasing magnetic field

B

and Lagrange multiplier

u

the ground state energy

E

will increase with increasing

u

and decreasing

B

the mean number of optical phonon

N

will increase with increasing

u

.