本論文是探討量子力學的物理特性與其在半導體元件上的模擬。為了描述量子力學模擬環境，首先我們必需開發一個有效率的特徵值與特徵向量的運算器來幫助我們解薛丁格波動方程式。這個高效率的運算器在本論文中稱之為QM-Solver。利用QM-Solver我們可以得到任意位能函數的特徵值和特徵向量，對於學習量子力學的原理，有很具體的幫助。其次，再配合我們建立的量子力學等效電路模型，來研究半導體元件中載子在量子井的運動情形。 In this thesis, we will study the quantum mechanics and its simulation on semiconductor devices. In order to handle the quantum mechanics simulation, we first need an efficient eigenvalue and eigenvector solver to help us solve the Schrödinger wave equation. This efficient solver in this thesis is called QM-solver. It is useful for us to study the quantum mechanics specifically by getting the eigenvalue and eigenvector from the QM-solver of any potential function. And the second, we use the equivalent circuit model of semiconductor device with quantum mechanics to observe the charge distribution in the quantum well.
