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. Recently

Mukhopadhyay and Chatterjee investigated the polaronic corrections to the first excited-state energies of an electron in a parabolic quantum dot using a canonical transformation method based on the Lee-Low-Pines-Gross formation. Using the Fock approximation of Matz and Burkey

Lepine and Bruneau discussed the effect of an anisotropic confinement on the ground-state energy of a polaron in a parabolic quantum dot. 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. The results indicate that the polaronic effects are more pronounced in quantum dots than those in two-dimensional and three-dimensional cases. Taking into (account) the electron-bulk LO-phonon interaction

Kandemir and Altanhan using 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. However

the properties of the strong-(coupling) polaron in the excited state in parabolic quantum dot has not been studied so far. By using the (variational) method of Pekar type

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

the average number of virtual phonons around the electron and the resonance frequency of polaron are (calculated.) Their dependence on the electron-LO-phonon coupling constant and the effective confinement strength is depicted. The (results) show that

with the increasing the effective confinement strength

the polaron binding energies in both the ground state and the excited state

the average number of virtual phonons around the electron and the resonance frequency of polaron in parabolic quantum dot are decreased. The average (number) of virtual phonons around the electron will increase with increasing the electron-LO-phonon coupling constant.