On the condition of electron-LO phonons weak coupling

the properties of exciton in parabolic quantum dot are studied. By using the linear combination operator and unitary transformation method

the ground state energy and the mean number of optical phonons in a parabolic quantum dot are calculated for the weak coupling exciton case. Numerical calculations are performed for GaAs semiconductor as a example and the results show that the mean number of optical phonons of weak-coupling exciton decrease with the increasing of the ground state energy and the confinement strength of quantum dot and increase with the increasing of the quantum dot radius.The ground state energy decrease with the increasing mean number of optical phonons and the coupling strength.