When we square the wave function, we obtain the probability
density. This graph is related to the probability of finding
the electron at each point in space. However, we measure over
regions in space. Fortunately, a little math can convert a probability
density in a region into a number representing the probability
of finding the object in that region. All of this is likely to
seem somewhat abstract. We can make it more concrete with the
Probability Illustrator program.
Click and drag the pencil that appears in the top frame to
sketch the wave function similar to the one in the
figure below. You need not sketch the wave function accurately.
Anything that looks similar is acceptable for our purpose. The
program sketches a graph of the probability density in the lower
Does the probability density graph drawn by the program seem
to be the square of the wave function that you sketched?
Now do the same for a wave function that is an approximate
reflection (about the x-axis) of the previous one. (Something
like the sketch below.)
How do the probability density graphs in the two cases, compare
with each other?
Is this result what you would expect? Why or why not?