
For simple potential energies, such as the square well, we can solve Schrödinger’s Equation analytically. One establishes regions in space by identifying locations where the total energy and potential energy cross, obtains the solutions in each region and adjusts parameters so that the boundary conditions match. The result of this process can be studied in most “Modern Physics” textbooks. Most real physical situations give rise to potential energies that are too complicated for easy analytic solutions. (In fact for many situations analytic solutions are not possible.) Thus, scientists resort to using computers to obtain numerical solutions to Schrödinger’s Equation. In this tutorial you will look at the basic procedures for obtaining physically acceptable, numerical solutions.