WarmUp Exercise #1, 8/24  (Assignment Due 8/26)

During the course of the semester we will integrate Physlet Quantum Mechanics (hereafter PQM) material into the lectures and the assignments.  As a consequence you should be looking at the text and applets where appropriate.  For example, if you are interested in learning more about "modern physics" or "old quantum mechanics," beyond what we did in lecture, you should look at PQM Chapter 3.  This is especially true in regards to the Bohr model. 

For Thursday, we will be easing into true quantum theory with a discussion of necessary classical ideas that will make QM a bit easier to digest over the course of the semester.  We will also start with a description of the various formulations of QM.  You should look over PQM 4.8-4.10 (including web stuff).

Questions regarding CLASSICAL probability distributions:

1. In your own words, what is a probability distribution? 
2. What is the difference between a relative and a normalized probability distribution?
3. Consider a classical particle, with an initial velocity, v, confined to move freely in a well of length L (there are infinite walls at x = 0 and x = L.  What does the particle's relative probability distribution (both in position and velocity) look like?  How would you normalize both relative probability distributions?
4. How would your answer to 3 change if the particle was in an x² potential well?

Answer in the form below, a short answer for each is fine. 
This report is due by 8:00 am Thursday morning.