Introducing Wave Function

Because matter waves are abstract ideas used to describe results, they do not travel through a medium, such as water. In fact, a matter wave is not a physical entity at all. So, scientists generally describe these waves in terms of mathematics or pictures. (We will use the pictures.)
 
Physicists call the pictures or equations wave functions. A sample of a wave function of an electron is shown below. The shape of the wave function is NOT the path that the electron traverses. It is a useful description related to the location of an electron and can be used to predict the probability of finding the electron in any given region of space.
 

Example of a wave function for an electron.

 

To understand how a wave function is related to probabilities we return (one more time) to the electron interference pattern and to the plastic waves. The places where electrons are most likely to be correspond to places where the two waves on plastic added and the amplitude was large. The locations where the probability of finding the electrons is zero correspond to locations where the waves on plastic amplitudes added to zero. In turn the plastic waves each represent part of an electron’s wave function. Their addition is the wave function at the screen. A large amplitude is related to a large probability while a small amplitude goes with a small probability.