1a) Griff. 9.8. Also: As you increase temperature, which begins to dominate more and more, spontaneous or stimulated emission? (Briefly, why?)

b) 9.9. Also: Why do people refer to tau as the average (or mean) lifetime of state b? (Show it mathematically)

2) 9.10, but only do the l=1, m=+/-1 states, since I did 2s and 2p (m=0) in my notes.

Note: The answer comes out the same for all the l=1 states, but the math is a little different for m=+/-1 and m=0. There's no handwavy argument, you must do the integrals.

3) 9.13. Also: The lifetime comes out a couple of orders of magnitude larger than in problem 10. Briefly, give physical reason(s) why.

4) 9.16

Hint: for part b, see Griffiths' formulas 9.84 and 9.85.

5) 9.19 a and c only. (Just use the exact result he gives in part b)

Hint: For part c, to use first order perturbation theory, you must write H = H0 + H'(t),

i.e. you must separate out the time independent part H0. Then you know exactly what the states a and b are, and what their energies are (and thus what omega_0 is.) Then you can use 9.17, i.e. usual TDPT to find the probability of flipping from up to down...

(Watch signs, spin up is NOT the ground state)

Don't forget to answer Griffith's final question in part c - how small must B0 be in order to believe your perturbation theory answer?