Seven down, two to go

The news in brief is that I passed my qualifying exam on Monday.

The exam was not exactly as I had expected.  The questions were a little easier than I had prepared for, though the same level as previous students' (in fact, the same as questions I know others have received).  The problem was that I made more silly mistakes than I should have and didn't feel as clever as I would have liked.

My prepared question on the de Haas - van Alphen effect was fine.  I think one of the professors was a little surprised by the way I approached it, but not excessively so and I was able to explain the difference between my way and the way he probably thought he would see (the way I showed works in more cases, but gives slightly less information).

My first on-the-spot question began with a very easy derivation (phonon dispersion on a 1D lattice).  The professor then asked me to show what the dispersion would look like if every second atom was different.  This is easy: the Brillouin zone shrinks by a factor of two, but in the heat of the moment I shrunk it in the wrong way (from just one end instead of symmetrically from both).  I should have worked out what was wrong more easily, but it's fair to just chalk it up to the pressure of the situation.  They then asked me how one would measure phonon dispersion in a real material.  I answered heat capacity, which is not entirely wrong, though neutron scattering would have been a much better answer.

My final question was to show that magnetic flux through a superconducting ring is quantised.  First the professor asked for the size of the flux quantum.  This threw me, not because it's obscure, but for quite the opposite reason: it's an important quantity and I felt like I should have known it by heart.  I decided to calculate it by dimensional analysis, but felt silly doing so, and was worried that I wouldn't have enough equations.  I wrote those I thought I would use, then said "sorry, I need to take a few breaths".  The professor said "what you're doing looks good", or something along those lines, which made me feel a lot better (it helped more than a few breaths would have), and it only took a couple of lines to get the answer.  There was a factor of 2 missing, which dimensional analysis can't give, but I knew it had to be there.  I knew exactly how to do the rest of the question, and although I made a sign mistake when writing down the expression for current, I knew something was not quite right and fixing it wasn't a big deal.

Writing about the exam makes me feel that I did a bit better than I thought when I came out!  I do think that the silly things I said or wrote were reasonable for an exam situation.

The title of the post refers to the nine requirements for a physics PhD from MIT: I have only the thesis defence and thesis remaining!