With the quick development of the semiconductor growth technology

people have produced kinds of quantum dots. Due to the novel optoelectronic properties and the transport characteristics of quantum dots

there will be a widely applied prospect for them. In recent years

the physical characteristic of a bound polaron in a quantum dot has been of considerable interest. Many investigators studied the properties of the bound polaron in a quantum dot by means of various theoretical and experimental methods. Recently

the properties of bound polaron in quantum dot were studied by using a linear combination operator method by the presents. However

the properties of the excited state of the bound polaron in a quantum dot have not been investigated so far. In this paper

the properties of the excited state of the weak-coupling bound polaron in a quantum dot were studied by using a linear combination operator and unitary transformation method.The relations of the vibrational frequency of the weak coupling bound polaron in a quantum dot with the effective confinement length of the quantum dot and the Coulomb bound potential are derived. Relation of the first internal excited state energy

the excitation energy and resonance frequency of the weak-coupling bound polaron in a quantum dot with effective confinement length of quantum dot

the electron-phonon coupling strength and the Coulomb bound potential are calculated. The numerical results show that the vibrational frequency

the first internal excited state energy

the excitation energy and the resonance frequency of the weak-coupling bound polaron in a quantum dot will increase strongly with decreasing the effective confinement length of the quantum dot and increase with increasing the Coulomb bound potential. The first internal excited state energy will increase with decreasing the electron-phonon coupling strength.