1i) Griff. 5.8

(For part a, please neglect the electron-electron interaction)

For 5.8b, give an explicit formula for the energies, including fine structure corrections, just like Griff. Eq'n 6.66. Basically, you have to think where/how factors of "Z" enter that formula. (Please show or explain your work)

ii) Griff. 7.6

2) Griff. 5.10a only. (We'll do some of this in class, but I'd like you to work it all out, basically confirm that my notes are right. You're free to use MMA to do parts of this, if it helps you.)

3) Griff 5.9

(Note: Griffiths is being a little vague. What he really wants is for you to figure out what the lowest couple of levels are - how would you label them? What do the wave functions look like? What is their spin? What is their degeneracy? Are they ortho or para? In all cases, tell which is higher in energy, ortho or para? Can you say why, briefly?

A well labelled energy level diagram of the lowest levels would also be worth many words here. It's a little hard to know what exactly happens in part b for excited states, but say whatever you can...)

4) What happens to the lowest state of ortho-helium when you put it in a large external magnetic field? (Work it out - how many lines does it split into, with what splittings? )

Hint: Griffiths' Figure 5.2 tells you something important, namely, which of the seemingly degenerate levels is REALLY the lowest state of ortho-helium. That'll help here! Also, Griff. section 6.4 showed what happens when hydrogen is put into a magnetic field. What's different, for Helium?)

NOTE: If you want to get ahead, the first problem NEXT week will be Griff. 7.1b.