Determining Probabilities

In the Probability Illustrator the value of the wave function is displayed next to an arrow that is just below the wave function graph. A similar arrow below the probability density graph displays the value of the probability density at that point. You can move these arrows.

The lower graph displays the probability density of finding the electron at each point in space. To determine the probability of finding the electron in a region, move the two arrows at the bottom left of the probability density graph to any two locations. The probability of finding the two electrons between these two locations is displayed at the bottom left corner of the graph.

The probabilities are given as numbers between 0 and 1. A probability equal to 0 means that the electron will never be found in that region. A probability of 1 says that you will definitely always find the electron in that region. To see how these probabilities work record the probabilities of finding the electron in

a) About one-fourth of the screen on the left side.
b) About one-fourth of the screen on the right side.
c) The left half of the screen.
d) The right half of the screen.
e) The entire screen.

Do the numbers for (a) and (b) or (c) and (d) differ? If so, use the wave function to explore why?

Is the probability for the entire screen what you expect? Why or why not?