Spreadsheet Solutions
In the exploration, the computer had already been programmed to solve the equation. However, computers generally deal with numbers, so we needed to convert the time dependent Schrödinger’s Equation,


Into something a computer can work with. So, we approximate a derivative as a different, or


How well this approximation works depends on how rapidly Y(x) is changing and how close x2 is to x1. For a second derivative we repeat the process in equation (2). The end result is that Y(x) at one value of x can be appropriately terms of its value at other values of x. Many methods have been developed to make the numerical solutions accurate and computationally fast. Our purpose is to understand the principles, not the details of the various methods. So we limit ourselves to a simple method called Euler’s Method. In this method we determine the value of Y(x) by extrapolating for its value at a previous location. The basic scheme is summarized in Figure 1.