中文摘要：

量子点作为一种重要的低维纳米结构,近年来在单光子光源和新型量子点单光子探测器的研究引起了人们的广泛关注,对各种势阱中量子点性质的研究已取得了重要成果.但是大多理论研究都局限于无限深势阱,而有限深势阱更具有实际意义.利用平面波展开、幺正变换和变分相结合的方法研究了有限深势阱中极化子激发态能量及激发能随势阱形状和量子盘大小的变化规律.数值计算结果表明：极化子的激发态能量、激发能随势垒高度或宽度的增大而增大,原因是势垒愈高、愈宽,电子穿透势垒的可能性愈小,电子在阱内运动的可能性愈大,进而导致极化子的激发态能量和激发能均随势垒高度和宽度的增大而增大;极化子的激发态能量和激发能随量子盘半径的增大而减小,表明量子盘具有显著的量子尺寸效应;极化子的激发态能量随有效受限长度的增加而减小,原因是有效受限长度愈大,有效受限强度愈小,电子受到的束缚愈弱、振动愈慢、势能愈小,进而导致基态能量、激发态能量减小;同时由于激发态能量较基态能量减小慢,使得激发能随之增加.研究结果对量子点的应用具有一定的理论指导意义.

英文摘要：

Studies of single quantum state measurement and the relevant physics are very important for the fields of quantum information and quantum coupution.In recent years,quantum dots as information carrier have become a hotpoint of research.The study on quantum dot properties has atracted a lot of attetion and made a series of progress.In this paper,we formulate a theoretical method that can be used to investigate polaron properties in lowdimensional structures in finite depth potential well.We assume that an electron in a quantum disk which is in other medium is in parabolic potential field,but the effect of the medium on the electron in quantum disk is equivalent to a potential barrier with height V1 and width d.By expanding the finite height potential barrier as plane waves and Lee-Low-Pines unitary transformation for Hamiltonian,as well as variation for expectation value of Hamiltonian where trial wave functions are obtained by solving the energy eigen-value equation,the ground state energy,the first excited state energy,and excitation energy of polaron are drived.Numerical calculation by using polaron unit,numerical results indicate that the first excited state energy and excitation energy of polaron increase with increasing the width or height of the potential barrier,because the probability of electron penetrating potential barrier will decrease as the width or height of potential barrier increases,so that electronic energy,the first excited state energy and excitation energy of polaron all increase.Numerical results also show that energies mentioned earlier decrease with increasing radius of quantum disk,which illustrates that the quantum disk has obvious quantum size effect.It is also found from numerical results that the first excited state energy of polaron decreases with increasing effective confine length,it falls quickly when effective confine length is less than 0.3 and is a little change when effective confine length is more than 0.3.The longer the effective confine length,the more weakly the electron i