Issued Wed, Apr 1 Due Wed, Apr 8

Required reading for this week: Finish Ch. 18, start Ch. 20 (up to p. 328)

1) Gas 18-5

(Note the typo, it's an exponential of radius)

2) Gas 18-11

3) Evaluate the integral where

.

(This is the integral I will call "D": the answer is in my notes, on p. 185.

Of course, for credit, you need to show your work... You're welcome to use Mathematica, but you'll probably have to do the angular stuff first, at the very least...)

4a) Gas 18-3. It's easiest just to come up with the formula for the energy of the state in a magnetic field B. (Hint: Gas. Figure 18-3 is helpful here)

4b) Apply the variational technique (like we use in class for the He atom) to estimate an upper bound for the ground state energy of the H- ion (this is a single proton, Z=1, with two electrons). Your variational parameter should be, as usual, the effective (shielded) nuclear charge. (FYI - this is basically Griffith's problem 7-7, but Gas. has really done all the work for you!!)

Cultural Note: You should get an answer for the energy which is larger than -13.6 eV. This would imply that there is no H- bound state, because if the extra electron just flew away, it would leave behind a neutral hydrogen atom with lower energy! This is incorrect: our variational estimate is an upper bound, and the correct answer (obtainable with a better trial function) is indeed < -13.6 eV. Griffiths shows how to do this in his problem 7.16. He also mentions that H- is indeed barely bound (it has no excited states) He also claims it exists in great abundance on the surface of the sun.

Extra Credit: (As usual, if you do this, hand it in to me separately)

Gas 18-8