Issued Wed, Apr 15 Due Wed, Apr 22

Required reading for this week: Ch. 13 and Ch. 21

1a) In class last week we briefly discussed the concept of "muon catalyzed fusion". The idea is that you build a hydrogen molecular ion ( ), but use a muon instead of an electron. (The muon mass is 207 times the electron mass) What is the equilibrium distance, R, between the two protons in this muonic molecular ion? What is the binding energy of this molecule? (Does this molecule give a nuclear fusion basically as soon as it forms? Why/why not?)

1b) Make some "back of the envelope" type calculations to estimate the rotational energy associated with a water molecule. If a microwave oven operates at a frequency of 2.5 GHz, estimate the energy of a single microwave photon in the oven. Do these energies compare? Do you think the microwave oven is a "classical" or a "quantum" device?

2) Gas 13-6

3) Gas 13-8a and b

4a) We solved the Schrodinger Eqn for hydrogen using the gauge where Show that the gauge choice is completely equivalent.

Find the gauge function f(r,t) that connects them.

4b) Argue (in some way, it doesn't have to be mathematically rigorous!) that the function is proportional to a delta function, , if t is very large (and find the proportionality constant).

5) Gas 21-1