Well I feel accomplished! Yesterday night I did my last chunk of grading of the spring semester. I had my Statistical Mechanics final exam yesterday morning too. It went better than I expected, considering the fact that I had been doing pretty bad on the partial exams and on some of the homeworks.
There were three problems. The first problem was to consider an ideal spin-0 boson gas. We were asked to find an expression for the chemical potential, and then decided whether you can achieve Bose-Einstein condensation with that system. It was a straight-forward calculation. In the end I found that there could not be any condensation. The second problem was a two-cite Ising model. We were asked to find the susceptibility and the energy variance. At first I started to freak about about the susceptibility, since I had to calculate the average spin. But then I found an expression for the average spin; it was just the derivative of the free energy, which can be found easily with the partition function. Then I completely forgot that I wanted the susceptibility and carried on to the next part. This was my first silly mistake. I had to provided low and high-temperature behavior of the susceptibility and instead provided the analysis for the average spin. Oh well! The last problem was to consider a weakly damped one-dimensional harmonic oscillator. We had to find the spectral densities for the spatial coordinate and the momentum coordinate. I tried something, but to be honest I never fully understood this last part of the course. Partly because I did not cared (and I should have cared), and partly because It was something new and I felt it was a bit rushed (I know, that is a very lame excuse). Overall, I hope to pass the course, at least with the minimum. I have worst things to think about next semester...
But it was not until today early morning, around 2:12 AM, that I realized my second silly mistake. The Electrodynamics final exam had been on the day before yesterday. Again, three problems. The first was an easy question. My professor is an experimentalist, he works with x-rays at the National Synchrotron Light Source. In day during class he asked us what was the wavelength of one photon with an electronvolt of energy. It turns out that this is related to an expression that involves three fundamental constants: Planck's constant h, the speed of light c , and the elementary charge e. The answer is 1239.8 nm. The second problem was to reproduce the calculation of the electromagnetic fields of a charge particle in motion. The idea was to consider a charge moving with constant velocity along the x-axis and to calculate the field at a fixed point along the y axis by considering the fields in the rest frame of the particle and then Lorentz- transforming to the lab frame. It was straight forward. Finally the last problem was about an electric dipole that was rotating along the x-y plane with a given angular frequency and we were asked to calculate the radiation fields and the angular distribution of the radiated power. This expressions involve a unit vector from the source to the observer. Usually this unit vector is a position vector divided by its magnitude. But no sir, the gentlemen writing to you on this cloudy afternoon decided that the unit vector was just the sum of three unit coordinate vectors. For starters that is not even a unit vector! Everything depended on that unit-vector, so of course everything came out wrong; my power distribution was uniform... I did not realized what my mistake was until after a day. What makes me most angry is the fact that I knew it had to be wrong. But I continued on, lying to myself. It all sucks. Oh well, I had been doing better at E&M, so I expect to pass this class too.
Next Tuesday I have my last final, Quantum Mechanics. I hope I do not have to writ about my third silly mistake.
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