The properties of the excited state of the weak-and strong-coupling polaron in a parabolic quantum dot were studied by using the Huybrechts' linear combination operator and the unitary transformation method.The first internal excited state energy

the excitation energy and the resonance frequency of both the strong-and weak-coupling polaron in a parabolic quantum dot are derived respectively.First

we have investigated the properties of the excited state energy

the excitation energy and the resonance frequency of the weak-coupling polaron in a parabolic quantum dot.The relation of both the excited state energy with the effective confinement length of the quantum dot and the electron-phonons coupling strength and the excitation energy and the resonance frequency with the effective confinement length of the quantum dot.The results show that

the excited state energy will increase strongly with decreasing the effective confinement length of the quantum dot

and will increase with decreasing the electron-phonon coupling strength

and the excitation energy and the resonance frequency increase with decreasing the effective confinement length of the quantum dot.Second

the properties of the vibrational frequency

the excited state energy

the excitation energy and the resonance frequency of the strong-coupling polaron in a parabolic quantum dot are studied.The relation of these quantities with the effective confinement length of the quantum dot

and the electron-phonon coupling strength is discussed.The results show that

the internal excited state energy

the excitation energy and the resonance frequency will increase strongly with decreasing the effective confinement length of the quantum dot

and increase with decreasing the electron-phonon coupling strength

and the vibrational frequency increase with decreasing the effective confinement length and increase with increasing the electron-phonons coupling strength.