With recent rapid advances in nanofabrication technology it has become possible to confine electrons in all three spatial dimensions in semiconductors called quantum dots.The electron energy spectrum of such quantum dot is fully quantized.Such systems are of great interest in fundamental studies

as well as in practical applications for microelectronic devices.Electron-phonon interaction

which plays an important role in electronic and optical properties of polar crystalline materials in three dimensions

will have pronounced effects in low-dimensional systems as well.Recently there have been a considerable number of theoretical studies on the same effects including the confinement problem in quantum dot system.Zhu and Gu have studied the effect of an external magnetic field on zero-dimensional polarons in the weak-coupling limit using the second-order Rayleigh-Schrodinger perturbation theory

and found that for a strong magnetic fields

the cyclotron mass in a parabolic quantum dot is split into two cyclotron masses.Zhou has calculated both the ground state and the exited state energy of strong-coupling magnetoplorons in a disk-shape quantum dot with Peker-tape variational method.In this paper

we investigate weak-coupling magnetopolaron’s properties in a parabolic quantum dot by the linear combination operators in the first time.It is shown that the bound state energy and binding energy decrease with increasing the effective confined length of the quantum dot

and enhance with enlarging the cyclotron resonance frequency.The Fig.1 and 2 present that the magnetopolaron ground state energy

E

0

of parabolic quantum dot is as a function of the effective confinement length and the cyclotron resonance frequency.The Fig.3 and 4 indicate that the magnetopolaron binding energy |

E

b

| of parabolic quantum dot effect as a function of effective confinement length and the cyclotron resonance frequency.We can see that the confine effect of parabolic quantum dot strengthens the ground state energy and the binding energy.