With the technological progress in material growth

semiconductor quantum wells and heterostructures were obtained experimentally.There has been considerable interest in physical properties of low-dimensional material.Using perturbation method

Hai studied the energy and effective mass of polaron in Q2D system

in calculation

the interface phonon

3D bulk phonon mode

parabolic quantum wells

infinite and finite quantum wells have been taken into account.Zheng studied the ground state energy and effective mass of a Q2D polaron system in a QW by using a modified Lee-Low-Pines transformation.Mori and Ando obtained that the effects for electron and different phonon mode interaction have the same result as bulk phonon mode.Employing second order perturbation theory

intermediate coupling theory and interpolation formula

Sarma discussed the influence of electron-LO phonon interaction on the electronic properties of single two dimensional electronic slab.By using the standard perturbation theory within the Thomas-Fermi approximation

Comas and Rücker calculated self-energy of weak coupling polaron.Li investigated the Stark energy shifts of a bound polaron in a finite and infinite QW by means of perturbation-variation method.Ren carried out the Feynman-Haken path integral theory to calculated the ground state energy of polaron in parabolic quantum well.Eerdun studied the temperature dependence of properties of electron-bulk LOphonon interaction system in a quantum well within the electronic-magnetic fields along the growth axis by means of variational wave-function and harmonic oscillator algebra method and he also obtained the self-energy of the system at a finite temperature.