1) Griffiths 9.5

2) Griffiths 9.6. You should find both ca(t) and cb(t) to second order, as Griffiths asks, but to make life a little easier, you only need to verify that cb(t) agrees with the exact result, which you calculated last week. (The algebra to verify ca(t) is a little painful...)

3) Griffiths 9.14, parts a through d only.

Note: When Griffiths says "H' is constant" in part c, he means it is a constant in TIME, not necessarily in space.

4) Griffiths 9.17. (Note: You can use the result of problem 3, part c to help here! Do you see why?)

Also: Why did Griffiths specify V0 << E1? What is wrong if this is not satisfied?

5) Consider a harmonic oscillator with ,
(sorry, MS word troubles! The potential term there reads: (1/2) M omega^2(t) x^2)
where the frequency is itself time dependent: .
(Sorry again , that's supposed to read: omega(t) = omega_0 + (delta omega) * cos(2 pi f t) )
Assume, (both are constants), and neglect any terms in H that are manifestly of order (something small)^2.

Use the results of problem 3 (part d) to calculate the probability (as a function of time) that a transition occurs from the ground state to the nth level of the original (time independent) harmonic oscillator.

Also: which level(s) can you (in principle) make a transition to?

At what frequency, f, does the system really want to make those transitions?

Hint: Use the fact (we've seen this before!) that for harmonic oscillator wavefns,

(assuming n is not zero)