Recently

with the quick development of techniques to fabricate material

the physical characteristic of low dimensional material have aroused great interest.The properties of magnetopolaron in quantum dot has been studied by many theoretical and experimental method by many investigators.Zhu and Gu theoretically studied the effect of electric-fields on shallow donor impurities state in a harmonic quantum dot by using effective mass approximation method.The interaction of electrons

confined in a quasi-zerodimensional quantum dot and longitudinal-optical(LO)phonons

placed in a perpendicular magnetic field

was studied by Wendler

et al.within second-order perturbation theory.Magnetic field effects on strong-coupling polarons in a parabolic quantum dot were investigated by Zhu et al.with the Landau-Pekar variational treatment.Zhau and Gu calculated the ground state and the first excited state of the strong-coupling magnetopolaron in a cylinder-shaped quantum dot by using the variational method of Pekar type.Using a very simple trial function with only one variational parameter

the effects of the parabolic confining potentials and magnetic fields on the binding energy of hydrogen impurities in quantum dots were studied indetail by Nguyen et al.By using the method of few-body physics

Xie investigated the binding energy of the ground state of the D

-

centers in quantum dots in magnetic field.Chen et al.investigated the thickness effect on the shallow donor impurity-bound polaronic energy levels in parabolic quantum dot in magnetic fields by means of the Larsen method.However

the properties of the polaron and the magnetopolaron in quantum dot has not been investigated by a linear combination operator method so far.The ground state binding energy and the mean number of optical phonons in the cloud around electron of the polaron and the magnetopolaron in parabolic quantum dot were calculated by the method of a linear-combination operator by the present authors.The purpose of this present paper is to explore the effect of the magnetic field

B

the electron-phonon coupling strength α

the confinement strength ω

0

and the variational parameter p

0

on the properties of the weak coupling magnetopolaron in parabolic quantum dot.The relation between the vibration frequency λ and the interaction energy

H

int

of the magnetoploaron in parabolic quantum dot with the magnetic field

the confinement strength and the electron-phonon coupling strength were derived by using an improved linear combination operator method.Numerical calculations for GaAs crystal show that the vibration frequency λ and the interaction energy

H

int

of the weak coupling magnetopolaron in parabolic quantum dot will increase with increasing the confinement stregth ω

0

the vibration frequency λ will increase with decreasing the variational parameter and the cyclotron frequency

whereas

H

int

increases with increase of p

0

and

H

int

increases with decrease of ω

c

.