Here is the HOMEWORK for this week

1) This one is meant to be a quicky! (What's the formal definition of Hermitian? Write it out in integral form. Think about dummy variables...)

2) See Gas' hint. "Apply the Pauli principle" means you should think about what the symmetry of your "relative" wave function u(x) should be for identical fermions.

If V0 is very large, I get an energy of . (Do your factors of 2 all work out?)

3) You can just write down the answers in terms of the square well wave functions, but you have to think about what the symmetry does to restrict your allowed states.

4b) Careful about factors of 2 in your relations between x1,x2 <-> x,X,

and also between p1,p2 <-> p,P

Your result for part b better be consistent with part a, since you're solving the same problem two different ways!

5) This is a slightly challenging problem. (Not conceptually, but it may exercise your ability to do a bit of involved algebra) Don't try to do it "quickly", on scratch paper - be careful and neat, go slow, give yourself plenty of space, get the algebra right the first time! It helps if you set the problem up with bras and kets and simplify as much as possible before trying to evaluate any integrals.

Also, you DID all the relevant integrals last week, where you found <n|x^2|n> for a harmonic oscillator (use <V>=<H>/2 from the virial theorem and you can just write it down!), and you also (hopefully) found .

If you're stumped, Griffith's Ch. 5 covers this pretty nicely. (He doesn't specialize to a harmonic oscillator, but simplifies the result formally to single particle integrals that you can easily do)