Numerical Solution of Schrödinger Equation by using Crank-Nicolson Method

The Schrödinger equation is a fundamental equation in quantum mechanics that describes how wave functions evolve over time. The study explored specific focus on the Crank-Nicolson scheme, which is widely used and efficient method. By applying these methods to the one-dimensional Schrödinger equation, the work provided insights into the behavior of these systems. To confirm the accuracy and reliability of this method, a test problem is solved. The result obtained from numerical method is compared with analytical solution. The graph of compared result is shown with the help of computational software. The test demonstrates that the method is effective for solving the Schrödinger equation, even when an analytical solution is not possible or too difficult to obtain. Overall, the Crank-Nicolson difference scheme is a valuable tool for understanding the behavior of quantum systems and solving problems.