With the development of solid science theory and experimental technology

the properties of the bound magnetic polarons(BMP)in crystals have been of considerable interest. Many investigators studied the properties of the BMP by means of various theoretical methods and experimental methods. Wollf

et al

. investigated the BMP in semimagnetic semiconductors and the BMP in dilute magnetic semiconductors by the optical experiments.Heiman

et al

. observed the variational model of the bound magnetic polaron and Roman spin flip line shape. Larsen studied the upper bound to the polaron ground state in a magnetic field using the Feyman path-integral method; Zhou solved the effective-mass equation and calculated the magnetopolaron binding energy in the ground state and in the excited state as well as the resonance energy of the magnetoplaron by means of the variational method. Wang and his co-workers studied the ionization energy of bound polaron in a magnetic field in asymmetric polar semiconductor heterostructures by using a modified Lee-Low-Pines variational method. Chen

et al

. investigated the properties of the impurity-bound polarons in a parabolic quanrum dot and in anisortopic quantum dots in magnetic fields and then studied impurity-bound polarons in double quantum wells in magnetic fields. Umehara presented a theory for the BMP in diluted magnetic semiconductors by a modified molecular-field approximation; Recently

Nagaku studied the bound excitonic magnetopolarons. In the early 1970s

Huybrechts investigated the internal excited state of the bulk optical polaron by using linear combination operator method. Some properties of the surface magnetopolaron in polyatomic polar crystals were studied by means of a linear combination operator and a perturbation method by one of the authors. However

no one studied the BMP with the linear combination operator and perturbation method so far. In this paper

we investigated the vibration frequency and the ground state energy of the BMP with this method. Using the parameters and the coupling constant of the AgCl crystal and the RbCl cvrystal for the weak coupling and the strong coupling

we calculated the vibration frequency and the ground state energy of the BMP. The results showed that the vibration frequency of the BMP increase with increasing the magnetic field

and the ground state energy does nearly not change when the magnetic field is increasing.