以半顯隱Runge-Kutta及擬譜法求解薛丁格方程

Abstract

本論文使用半顯隱Runge-Kutta和擬譜法建立計算格式以求解薛丁格方程。利用補償法將邊界條件加入格式中，藉由離散的能量估計，訂立適當的懲罰參數。我們應用Legendre-Gauss-Lobatto 及Chebyshev-Gauss-Lobatto這兩組不同的網格點進行計算，並從幾個數值實驗來驗證此格式。

In this paper, we present a scheme for solving the Schrödinger equation based on Implicit-Explicit Runge-Kutta and pseudospectral method. The boundary conditions are imposed to the scheme through the penalty methodology. By conducting the energy estimate, we determine the values of penalty parameters. We apply Legendre-Gauss-Lobatto and Chebyshev-Gauss-Lobatto grid points for numerical computations. Several numerical experiments are shown to validate the scheme.