Issued Wed, Nov 6 Due Wed, Nov 20

Required reading for this week: Ch. 10 (Ch. 9 is optional, for now at least)

1) Use separation of variables in Cartesian coordinates to solve for a single particle in an infinite cubical well ("particle in a 3-D box"):

a) Find the stationary state wave functions, and corresponding energies.

b) Find the lowest 6 energies. (Call them E1, E2, ... E6)

Find the degeneracy of each of these energies.

(NB: Degenerate bound states don't occur in 1-D, but are common in 3-D!)

c) What is the degeneracy of E14? Why is this case interesting?

2) There are a number of equations in Gas. Ch. 10 which he just writes down and says "it is easy to show" or "it follows that", "and so on", etc. (the usual physics textbook-ese!) Please show the steps Gas left out to get the following statements:

Eq'ns 10-7

The unnumbered equation one line past 10-12

Eq'n 10-14

Eq'n 10-25

The unnumbered equation just after 10-26

The statement " =0", two lines above the paragraph above Eq'n 10-27

That (i.e. part of the "and so on" following 10-27.

Eq'n 10-43

(Since these are all "show that" problems, there won't be any hints this week)

Note: These problems are essentially pure math. You should be able to get them even if we haven't reached the eq'n in question yet in lecture. In fact, it should help the lectures make more sense if you've already proven these eq'ns ahead of time!