In recent years

the lots of novel effects of the quantum dots systems have attracted more and more physicists.Because of the wide device applications and a lot of new physical effects in such structures

understanding the electronic properties of these systems is of particular importance.Several studies have already been carried out on the interaction of the electrons with longitudinal-optical(LO)phonons in quantum dots.Kandemir and Altanhan used the Lee-Low-Pines transformation to calculate the polaronic effects for an electron confined in a parabolic quantum dot.Zhu and Gu investigated the ground states and self-energy of the weak-coupling polaron in a parabolic quantum dot by using the second order Rayleigh-Sch rdinger perturbation theory.Li and Zhu investigated the strong-coupling polaron in a parabolic quantum dot by the Landau-Pekar variational treatment.It is shown that both the polaron binding energy and the average number of virtual phonons around the electron decrease with increasing the effective confinement length.Other investigations indicate that the bound interaction of the Coulomb potential plays an important role on the property of optical polaron.Es-shai

et al

.investigated the impurity bound polaron in a cubic quantum dot using the variational approach.Melnikov

et al

.applied the adiabatic variational method to calculate the polaron energy shift in a spherical quantum dot.Satori

et al

.attained the binding energy of a bound polaron to shallow donor impurity in spherical quantum dot using a vatiational approach within the effective mass approximation.One of this paper's authors achieved the vibration frequency and the average number of phonons of the strong-coupling bound magnetopolaron in a parabolic quantum dot by using the linear combination operator and unitary transformation methods.In the present paper

by using the variational method of Pekar type

we have studied both the ground state energy and the excited state energy of strong coupling bound polaron in parabolic quantum dot.The polaron energies in both the ground state and the excited state

the average number of virtual phonons around the electron were calculated.Their dependence on the effective confinement strength and the Coulomb potential was depicted.