a. Click on "Position Graph" below the right-hand graph. The graph shows the probability that a particle is in the ground state at some position x. You may vary n to see higher energy states. Under the left-hand graph, a ball is bouncing back and forth between the two walls. What does the probability of finding the particle as a function of x look like for this classical case? Briefly discuss your reasoning. After you answer, click "Position Graph" below the left-hand graph and check yourself. Was your answer right or wrong?
b. Under what conditions would the right-hand graph look like the left-hand graph. In other words, what is the correspondence between the classical and quantum position probabilities of a particle in a 1-d box? Check your answer using the above "Position Graph" buttons.
c. Click on "Momentum Graph" on the right-hand graph. Displayed is a graph of the probability of the particle's momentum as a function of x. The box <p> gives the expectation value of the momentum of the particle. Now click on "Velocity Graph" on the left-hand graph. What is the difference you see? Why does this difference exist?
Script by Mario Belloni and Wolfgang Christian.
Questions by Larry Cain.
Java applets by Wolfgang Christian.