Studying

Tomorrow I have part III of my qualifying exam, so I thought I should tell you what our qualifying exams are about, what we study in condensed matter physics (the topic of this exam), and what my classmates and I have been doing to study.

PhD programs in the US typically include a qualifying exam.  This covers the subject in which the PhD is to be awarded, to make sure a student knows more than just how to do research.  This may be done in conjunction with the course requirement, either by covering different areas to get the full breadth without duplication, or by making sure that the courses are tailored towards teaching what is tested on the exams.  Or, as a third option, they could be combined with no thought at all.  MIT physics does primarily the first, and to some extent the second.

The first qualifying exam is taken in August of first year, on the first day of orientation.  It contains 20 short questions covering a wide range of undergraduate physics, in classical mechanics, quantum mechanics, statistical mechanics, and electromagnetism.  The pass mark is something like 55%, and approximately two thirds of students pass on their first attempt (the pass rate goes up on subsequent attempts).

I took the second qualifying exam in January of my first year, a typical time for theorists.  It contains 4 questions, one on each of the previously mentioned areas of physics.  I suspect the pass mark is only around 4/10 on each question - each question must be passed individually - though probably four 4s wouldn't be sufficient overall (the 55% for part I I heard from MIT - this one is more rumour).  I actually found this easier than part I, because there were fewer questions and once I understood one it was reasonably straightforward.  I think I did well on the test, though we only receive a pass/fail grade.  Once again, about two thirds pass on first attempt.

Part III covers our specialty area, e.g. condensed matter theory, condensed matter experiment, high energy theory...  It is an oral exam given by a committee of three professors from that area of physics.  One question is given a week in advance, and the others are on the spot.  This time the pass rate is more like four out of five, though I have heard that condensed matter experiment had a tough year this time, I don't know why.

Condensed matter theory is based mostly on the theory of solids I and II I took during first and second years.  A graduate solid state physics sequence covers approximate the following topics.

*A classical description of solids (especially metals), and how far that can take us, and what additional information we get from the simplest possible insertion of quantum mechanics into this picture.
*A description of crystal structure and symmetries.
*An introduction to methods of calculating the possible energies of electrons in crystals (this is the largest part of the first semester).
*How to measure the same thing to check our calculations (there is a beautiful method called the de Haas - van Alphen effect, and my prepared question focuses on this).
*How atoms vibrate in solids (the second big chunk of the first semester).
*The response of electrons to each other and small perturbations (a big part of the second semester).
*The response of electrons to electric and magnetic fields (this shows up everywhere, but one particularly sophisticated example is the quantum Hall effect).
*Superconductivity (the middle big chunk of the second semester).
*Magnetism (the last big chunk).

Additionally, we are expected to know some thermodynamics and statistical mechanics, but these are covered in a different course.

Jimmy, David, Ognjen and I began our study in January by reading Ashcroft and Mermin's standard solid state physics textbook.  We read eight chapters a week, so we finished in early February.  For a few more weeks we gave presentations on particular areas we wanted to understand better: for example, I showed why the BCS ground state is superconducting.  During the final third of our study, we've been asking each other questions, trying to anticipate what the examiners might ask (that's not too difficult, because we have talked to past students), or even go a little beyond so that the exam is easy by comparison.  Early last week and late the week before, we gave full mock exams.

So far, the study has paid off: David is the only one to take his test, and he passed.  I will keep you updated!