Saturday, February 20, 2010

Back from the Dead

Part of the reason we were so quiet In November and December is that I was studying for (and passing, apparently) my qualifying exams. I had meant to say something about this just after I had taken them, but didn't finish the post, and eventually forgot about it with all the other craziness going on at the time. I'm glad to finally be done with the exams, as this means I can actually get some useful work done at home and on research. On the other hand, it's sort of a weird feeling no longer having any major deadlines looming over my head for a few years.

Qualifying exams are odd beasts. For us, there are two exams, "Classical" and "Modern," each 5 hours long. I have to pass them separately, so if I pass one and fail the other, I only have to retake the one I failed. I get one more attempt, if necessary, in the spring. What is most odd about the exams is the split. "Classical" normally means "not quantum"; in this context it means "pre 1900." And even then, the split is not perfect.

Our classical exam has mechanics (ie, analytical/Newtonian), electrodynamics, and statistical mechanics. Stat mech contains thermodynamics, which I suppose is why it gets put under classical, but it also contains quantum statistical mechanics, which should definitely go under modern. What you end up with is that a single problem could be split between the two exams, with the stat mech part giving you a result and having you carry out further derivations from that point, and the quantum part deriving the result the stat mech part took as given.

Our modern exam has quantum, special relativity, and math methods. The math that physicists use all predates 1900, but a lot of the higher-level stuff gets used primarily in quantum, so that's why it's on the modern exam. Special relativity really ought to be under electrodynamics, but the grad-level discussion of it does start to pull in some of the more difficult math, so some (I emphasize "some") relativity problems aren't too out of place on the modern exam.

What was weirdest for me was the actual set of problems that showed up on my exams: the difficulties I had in the problems seemed very low-level. On the classical exam, only two problems gave me any real trouble. One was a thermodynamics problem involving a derivation I hadn't seen since second year of undergrad. The other was a statistical mechanics problem that really amounted to a series of increasingly complicated infinite series. The major difficulty was keeping track of all the terms (though to be fair to the problem, I think there is a MUCH simpler way of doing it if you remember some stat mech cleverness, which apparently I don't). And since we only had to do seven problems, I didn't really have to worry about them. As it turns out, I didn't quite finish two of the other problems, because I made similar stupid mistakes at the end of both of them, and forgot that the last part of each problem was really as easy as it apeared. Two of the modern problems were trivial math problems, which was a little disconcerting. All the other problems on that exam were good, but I was a little surprised at the lack of problems requiring matrices and state vectors. One of the relativity problems used the electromagnetic field tensor, but nearly all of the quantum problems were written so as to favor solving partial differential equations. I guess in sum, the quantum was more Schroedinger and less Heisenberg than I anticipated. Which is a little weird because usually the Scroedinger approach is taught earlier, and the Heisenburg (and Dirac) approach is only taught on the student's second or third pass through Quantum Mechanics.


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