One year down...

... and so many to go. Today I had my last final examination of the spring semester, on Quantum Mechanics.

Overall it was a fair examination. I think some of the problems involved a significant amount of tedious algebra. I finished 15 minutes early, but I did not worked on the last problem, and I deserved it. The first problem was a harmonic potential along the z- axis define on a square region of the x-y plane, outside this region an infinite potential in the x and y directions. We were asked to find the energy eigenvalues and normalized eigenfunctions, but I could not recall the functional form of the harmonic oscillator eigenfunctions. I learned them at some point and I got used to reading them from textbooks, so I could not remember from the top of my head. Oh well. This makes me a tad annoyed, since the professor did not allowed a formula sheet. If I were stranded on a deserted island with no books or any food, I think the first thing on my mind will be to get something to eat, not doing any physics. But maybe that would be the fundamental difference between me and "the good students"; they choose physics above personal satisfaction.

Anyways, the second problem was about time-dependent perturbation theory. We had a potential that was turned on and was cubic in x and decayed exponentially in time. The system was a harmonic oscillator. We were asked to find the probability to have transitions to any state starting in the ground state. It took me a while to remember the expression for the first order correction, but at the end I think I got it. I was happy with my self, since I was able to write the cubic x term in terms of the creation and annihilation operators and the number operators and this time I got something that was really easy to finish. I remember one homework we had a cubic term and I did not simplified it enough. But thankfully I had the idea to write everything in terms of the number operator and the made it easy to realized only two terms survived. The third problem was two identical fermions in an infinite well potential and we were asked to consider the spatial wavefunction for the triplet and singlet spin states. Finally, the last problems were about a constant potential radial barrier, and we had to answer some questions about phase shifts. I knew this question was coming and guess what? I did not study for it. The last week of classes were really hard on my sleeping, so I was half awake during class; and I just thought it was a complicated topic for an exam. Wrong! None of those is a real reason not to studied. I never learn my lesson, it is a good thing that I could not answer that last question, because I did not deserved to done well.

All is done, I passed Statistical Mechanics with a B+. I finished my finals. I can relax. Meri is coming tomorrow and we might go to New Haven for some exploring. Today I will try to start with my summer self study: Quantum Field Theory, basic String Theory and a big load of Mathematics!