1) Griff 6.18

2) Griff 6.20

3) Consider the (eight) n=2 states of hydrogen. You can identify them as or , whichever basis is more appropriate, in the following two parts. (Please be clear which basis you use in each part.)

a) What is the spectrum when the atom is placed in a weak external magnetic field, B? (Weak compared to your answer to problem 1, say)

Show your result in an energy level diagram just like Griffith's Figure 6.11.

Please label the state and starting energy (at B=0) of all lines clearly.

What is the slope of the lines?

b) What is the spectrum like when the atom is in a very strong external field, B? (Show your results just like you did in part a) You may assume the field is so strong that you can completely ignore any fine-structure splittings. Label the state of each of your lines clearly. What is the slope of the lines now, for large B? What is the degeneracy of each line you draw?

c)You do not have to write this up or turn it in; it's not extra credit, but just to think about:

As the external field increases, the graphs in parts a and b should "merge into" one another. That is, if you extended your x-axis in part a, you could have put BOTH graphs on one single plot. But, how does this work? The number of lines you have in part a don't even match the number of lines in part b...And, the labelling of states is different. How can that be? How does everything match up? (This is, in part, the topic of Griffiths' section 6.4.3, although at a qualitative level you should be able to think about how the matching can occur without solving any equations at all.)

4) Griff 6.26