## Classical / Quantum Exercise #1

#### Please answer the following 3 questions
regarding the Physlet:

#### 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.