Numerical Solution of Schrödinger Equation by Crank–Nicolson Method.

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. [ABSTRACT FROM AUTHOR]