Numerical Solution of Schrödinger Equation by Crank-Nicolson Method

Abstract

In this study, we implemented the well-known Crank-Nicolson scheme for the numerical solution of Schrödinger equation. The numerical results converge to the exact solution because the Crank-Nicolson scheme is unconditionally stable and accurate. We have compared the results for different parameters with analytical solution, and it is found that the Crank-Nicolson scheme is suitable for the numerical solution of Schrödinger equations. Three different problems are included to verify the accuracy, stability, and capability of the Crank-Nicolson scheme.