When physicists wish to describe or predict the motion of large objects, they work with some basic concepts such as Newton’s Laws. They consider the forces or energies involved, then write equations, draw graphs and predict changes as the object moves through time and space.

Predicting probabilities for small objects is somewhat similar. The basic concept is Schrödinger’s Equation, named for Erwin Schrödinger who first wrote it. This equation describes the changes in wave functions over space and time. It is based on the wave behavior of small objects and conservation of energy.

The mathematical form of Schrödinger’s Equation is a little complex, so we will not write it down. Instead we will introduce a series of steps based on the equation. These rules will enable you to sketch wave functions for several situations, then interpret the results in terms of probabilities.