Quantum Mechanics Homework #1

Well, in the past two days I’ve linked to an Internet quiz and some anime videos, so in order to retain my street cred in the Faculty Lounge, it’s time to post a homework assignment. Don’t worry: if you haven’t met me in person, there’s no way I can grade you on it (unless our quantum states are somehow entangled). This problem set covers everything in our first two seminar sessions on QM, except for the kaon physics which we did as a lead-up to our next topic, Bell’s Inequality. I’ve chosen six problems, arranged in roughly increasing order of difficulty. The first two are on commutator relations, the third involves position- and momentum-space wavefunctions, the fourth brings on the harmonic oscillator (with some statistical mechanics), the fifth tests your knowledge about the Heisenberg picture, and the sixth gets into the time evolution of two-state systems.

Without extra ado, then, I give you Quantum Mechanics Homework #1.

People’s vacation schedules and the NECSI summer program are messing up the orderly progression of our seminars, but that’s OK — it just means those who want to do their QM homework have an additional week to enjoy the puzzles I’ve set for them. Our next meeting will be a week from today, when Ben will discuss certain tools used to measure the complexity of, er, complicated systems as a function of scale.

We have at least two lectures left on the quantum material, although scheduling difficulties may prolong the time it takes us to cover them. The next, as I mentioned earlier, will be on Bell’s Inequality, and the one after that will bring us into quantum decoherence. (Shh: foreshadowing the topic of decoherence is why I introduced coherent states in problem 5, but don’t tell anybody.)

2 thoughts on “Quantum Mechanics Homework #1”

1. Donâ€™t worry: if you havenâ€™t met me in person, thereâ€™s no way I can grade you on it (unless our quantum states are somehow entangled).

the [class after next] will bring us into quantum decoherence.

Going by your post on the quantum mind (and only by that — I have zero knowledge of QM), it may be because of decoherence that our states aren’t entangled, and thus that you probably won’t grade me. If so, praise decoherence.