With the development of molecular beam expitaxy(MBE) technology and metal organic chemical vapor deposition(MOCVD) technology

there has been great interest in investigating quantum dot in both material science and condensed state physics field.Due to size of quantum dot was small

they had a series of new and serious character

for example

quantum size effect

quantum coherent effect

quantum tunnel effect

Coulomb resistance effect and surface effect

etc.

these had brought infinite chance and hope on development and use of new materials.The properties of the polaron in a quantum dot have been studied by many investigators theoretically and experimentally.In recent years

with the study of the properties of bound polaron in a quantum dot

people have paid more attention to them.The vibrational frequency

the average number of optical phonons and the interaction energy of bound polaron in a parabolic quantum dot have been discussed using the linear combination operator method by the present authors.However

the properties of excited state of bound polaron in a quantum dot have not been investigated by a linear combination operator method so far.The purpose of the present paper is to explore the effect of Coulomb bound potential on the properties of the bound polaron in a quantum dot.With the strong-coupling between the electron and bulk LO phonon included

we obtain an expression for the vibrational frequency

the first internal excited state energy

the excitation energy and the resonance frequency of the strong-coupling bound polaron in a quantum dot by using the linear combination operator method.The relation of these quantities with the effective confinement length of the quantum dot

the Coulomb bound potential and the electron-phonon coupling strength were discussed.Numerical calculations show that the vibrational frequency

the first internal excited state energy

the excitation energy and the resonance frequency of the strong-coupling bound polaron in a quantum dot will strongly increase with decreasing the effective confinement length of the quantum dot

and will increase with increasing the Coulomb bound potential and the electron-phonon coupling strength.