A Modified Crank-Nicolson Method for Numerical Solution of the Linear Time-Dependent Schrodinger Equation

Abstract

This paper presents the effectiveness of the solution of the time-dependent Schrodinger equation using the modified Crank-Nicolson Method (MCNM). The method was developed through finite difference approximation. To demonstrate the effectiveness of this approach, three different problems were tested with these approaches by using MATLAB soft code. Also, this research verifies that, in the presence or absence of potential energy, the modified Crank-Nicolson method for solving the time-dependent Schrödinger equation is accurate, convergent, and computationally efficient.