FEW BODY PROBLEM IN NANOCRYSTALS

我们从理论上研究了纳米晶体中电子-空穴系统的量子力学态和动力学。主要结果如下。(1)我们建立了一种有效的方法来计算球形量子点中电子-空穴对态的所有本征态。这使得计算每一个总角动量的本征态，并成为数值方法的基础，研究对任意扰动的响应。(2)用我们的理论分析了CuCl纳米晶在NaCl晶体中的瞬态吸收光谱和双光子吸收光谱的实验数据。测量结果与理论计算结果吻合较好。(3)研究了位于量子点外部的点电荷对真实的材料中观察到的持续烧孔的影响。(4)通过数值计算研究了球形量子点表面电子空穴对的本征态。还阐明了均匀磁场的影响。(5)利用简单的两粒子束缚态模型研究了复合粒子的量子隧穿。结果表明，即使在单个势垒的情况下，也可能发生共振隧穿。

We have investigated theoretically quantum mechanical states and dynamics of electron-hole systems confined in nanocrystals. The main results are as follows.(1) We have established an efficient method to calculate essentially all of the eigenstates of an electron-hole pair state confined in spherical quantum dots. This allows for calculation of eigenstates of every total angular momentum, and becomes a basis of numerical method to investigate responses to arbitrary perturbations.(2) The experimental data of transient absorption and the 2-phohton absorption spectra obtained for CuCl nanocrystals embedded in NaCl crystals are analyzed by our theory. Good agreements between the measurements and the theoretical calculations are obtained.(3) The effects of a point charge located outside of quantum dots are investigated in connection with the persistent hole burnings observed in real materials.(4) The eigenstates of an electron-hole pair confined to a surface of spherical quantum dots are investigated by numerical calculation. The effects of a uniform magnetic field are also clarified.(5) Quantum tunneling of a composite particle is investigated by a simple two-particle bound state model. It is found that resonant tunneling may occur even in the case of a single potential barrier.