The properties of the polaron in crystals influence the properties of crystals very remarkably. The properties of the polaron for polar crystals have been of considerable interest.The polaron problem has been studied by many theoretical and experimental method by many investigators.Huybrechts calculated the ground state energy of the polaron. By means of vibrational scheme

the ground state energy

the effective mass and the mean number of phonons of polaron are derived by Tokuda. We discussed magnetic field and temperature-dependence of a magnetopolaon by using a Tokuda's method. The polaron features of the one-dimensional Holstein model are investigated by Cataudella

Filippis and Iadonisi by improving a variational method introduced recently and based on a linear superposition of Bloch states that describe large and small polaron wave functions.The mean number of phonons are calculated and discussed.However

the research on the magnetic field and temperature-dependence of the mean number of phonons in a magnetopolaron has not been studied so far.In this paper

the magnetic field and temperature-dependence of the mean number of optical phonons for a magnetopolaron in polar crystals are investigated by using a linear combination operator method.The results show that for the weak coupling the mean number of optical phonons

N

will increase with increasing temperature T vibrational frequency λ and magnetic field B and will increase with decreasing coordinate z

whereas for the strong coupling will

N

increase with increasing λ

z

B and T.