In recent years

with the development of semiconductor growth technology

people have producedsome kinds of quantum dots. The novel optoelectronic properties and the transport characteristics of quantum dots will be a widely applied prospect.The interaction of of the electrons with longitudinal-optical(LO) phonons in quantum dot have attracted more physicists because of the electronic properties of particular importance.The more physicists have studied the polaron in quantum dots by a lot of method. The properties of bound polaron in a parabolic quantum dot have been discussed using the linear combination operator and the unitary transformation method by the present authors. However

using Huybrechts method

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

the ground-state energy

the first excited-state-energy

the transition energy from first excited -state to ground-state and transition frequency were derived by using the Huybrechts method. Two limiting cases were discussed. Firstly

we investigated the transition energy and the transition frequency of the weak-coupling polaron in a semiconductor quantum dot.The numerical results showed that the transition energy and the transition frequency increases with decreasing the effective confinement length.Secondly

we investigated the transition energy and the transition frequency of the strong-coupling polaron in a semiconductor quantum dot. The numerical results showed that the transition energy and the transition frequency increases with decreasing the effective confinement length of quantum dot .The transition energy and the transition frequency of weak- and strong-coupling polaron in a semiconductor quantum dot decreases with increasing the electron-phonon coupling strength.