摘要
不含時薛丁格方程式為物理學的基礎方程式之一，傳統方法都是將此問題視為矩陣特徵值問題以有限差分法求解，而在本文裡將提供一個新的方式解決此問題，直接將對應的能量泛函極小化，也就是說我們將此問題的能量泛函視為最佳化的問題裡的適應函數，然後使用粒子群演算法計算出最小(波函數)以及對應的適應函數值(能量)，最後在使用繪圖處理器協同運算，加速程式執行效率。

Abstract
The time-independent Schrödinger equation is one of the fundamental equations in physics. The conventional method for this equation is to solve an eigenvalue matrix problem derived from some discretization methods, such as the finite difference techique. In this thesis, we demonstrate a novel way to solve such problem. We directly minimize the corresponding energy functional. That is, we treat this essential problem as an optimization problem and the energy functional is the fitness function. We particularly employ the particle swarm optimization method to obtain the minimizer (wave function) and the corresponding fitness function value (energy). Finally, we also use the graphics processing unit to accelerate the computation of this problem.

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