Because nanometer materials is smaller

they possess rich scientific meaning and quantum effect. Base on quantum effect of these materials

develop a series new materials on photoelectron

photon and related quantum parts

bring about new trend on study and development of materials science. Quantum dot is very special because it's confined in three-dimension

quantum effect is more obvious

and become a new study realm. The structures of quantum dots were studied by perturbation method

varational method

and a few bodies method

base on effective mass approximation. E. Peter

et al

. report on the observation of asymmetric phonon sidebands on both the exciton and biexciton emission lines in single GaAs monolayer fluctuation quantum dot

and indicate that the contribution of phonon sidebands to the emission line is larger for the biexciton than for the exciton. R. P. Wang

et al

. studied Raman spectra of InO power and free-standing nanowires prepared by ablation. They found that the coupling strength determined by the ratio of second-to first-order Raman scattering cross sections diminishes with decreasing nanowire diameter

and the Frohlich interaction plays the main role in electron-phonon coupling in InO. J. L. Chen

et al

. studied the spin-relaxation time due to the electron-acoustic phonon scattering in GaAs quantum dots by exact diagonalized the electron Hamiltonian with the spin-orbit coupling

and discussed different effects such as the magnetic field

the quantum dot size

and the temperature on the spin-relaxation time.In this paper

the properties of polaron with electron-LO-phonon weak-coupling in cylindrical quantum dot

which was in quantum well and parabolic potential

were investi-gated by using the linear combination operator and unitary transformation methods. The results indicated that the renormalization mass of polaron in quantum dot decrease with increasing cylinder height

and increase with increasing coupling strength because of interaction between electron and crystal vibration. Ground state energy has something to do with size of quantum dot

characteristic frequency

coupling strength

and magnetic-field strength

etc

.

it increased with decreasing cylinder height and increasing characteristic frequency

magnetic-field strength.