Classical / Quantum Exercise #1

 Position Graph Velocity Graph n = Position Graph Momentum Graph

Questions

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?

Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Larry Cain.
Java applets by Wolfgang Christian.