I am done with classes for the rest of the (calendar) year! Although I still have one more semester to finish my first year in graduate school, I feel happy for the temporary calm. Today we had the last lectures on Classical Mechanics and Electrodynamics.
Mechanics treated the infinite-degrees of freedom system, and we considered a case where we got equations that were completely similar to field equations. We define the functional derivative and the professor discussed a bit the road that leads to the Quantum Field Theory.
In Electrodynamics we discussed various topics. First we considered some naive arguments about superconductivity, and discussed the London equation and the Landau argument of the macroscopic extent of the wave function. We arrived at the quantum of magnetic flux, then my professor discussed Dirac's argument about electric charge quantization in the present of a magnetic monopole field and how an experiment by Cabrera displays one event that is candidate for a magnetic monopole. All in 55 minutes!
NO MORE HOMEWORK!!!!
I guess tonight is going to be easy and light. I am doing laundry now, after some end-of-classes celebration in a nearby brew house with other graduate students.
15 December 2006
12 December 2006
First Final
That sounds paradoxical, but today I had my first final exam of the semester. It was on Quantum Mechanics.
As usual, time was the biggest factor. The exam consisted of 4 problems. The first problem was about coherent states. Given a coherent state \ket{\alpha} we were asked to find its normalization and expectation value of the square of the position and momentum variance. I am pretty sure it was not as long as I made it. It involves lots of creation and annihilation operator algebra. Very tedious for a timed exam. The second problem was to calculate the approximate energy eigenvalues given the potential using the WKB quantization condition. It was easy. I was a bit clueless for the third problem: two infinite solenoids, with opposing currents, and electron beams that passed in their vicinity. We had to compute the interference pattern for one path vs. the other path. Sadly, I did not read much on the Aharanov- Bohm effect, so I left it for the end and had no time to work on it. The last problem was our good old friend the infinite square-well, finding the propagator. It was a bit tricky, since I was a bit confused with the units of the energy levels. But I quickly re-derived everything and confirmed that my memory was right.
Should be well! I hope I pass this class, so I can start with the good stuff.
As usual, time was the biggest factor. The exam consisted of 4 problems. The first problem was about coherent states. Given a coherent state \ket{\alpha} we were asked to find its normalization and expectation value of the square of the position and momentum variance. I am pretty sure it was not as long as I made it. It involves lots of creation and annihilation operator algebra. Very tedious for a timed exam. The second problem was to calculate the approximate energy eigenvalues given the potential using the WKB quantization condition. It was easy. I was a bit clueless for the third problem: two infinite solenoids, with opposing currents, and electron beams that passed in their vicinity. We had to compute the interference pattern for one path vs. the other path. Sadly, I did not read much on the Aharanov- Bohm effect, so I left it for the end and had no time to work on it. The last problem was our good old friend the infinite square-well, finding the propagator. It was a bit tricky, since I was a bit confused with the units of the energy levels. But I quickly re-derived everything and confirmed that my memory was right.
Should be well! I hope I pass this class, so I can start with the good stuff.
07 December 2006
Done for the week!
I am done with homeworks for this week! It might not seem like much, since tomorrow is Friday. Still, some of the past weeks I have spent most of Friday evening's working on the Classical Mechanics problem sets that are done on well, Fridays.
On Sunday I worked on the Classical Electrodynamics homework assignments. We are not studying electromagnetic waves. Most of the problems were about calculating transmission and reflected coefficients with two interfaces of materials. These problems have an awful amount of algebra with the boundary conditions. It was sad that I was not able to worked out all the cases for the last problem. Oh well! I am doing pretty bad on this course, so I have a feeling I am going to have to repeat it next fall, which is a bit annoying considering that I have to catch up on some fancy Theories...
After I handed the E&M problem set on Monday, it was time for Quantum Mechanics. Three problems, mostly on electromagnetic terms in the wavefunction (gauge invariance). The first one was about a magnetic monopole. The second problem was about the spin precession of an electron in a uniform magnetic field and the last problem was to calculate a commutator for the x- and y- components of the mechanical momentum. This problem set took a while since I was just out of it thinking of crazy things that were not helping. I handed the quantum problems today.
Finally Classical Mechanics! This time it was on fluid dynamics. Two problems, one to determine the free shape of a fluid rotating in a cylindrical vessel. The other was to find the velocity profile for a sphere submerge in a flowing fluid with constant asymptotic behavior. Fun, fun!
Two homeworks left for this fall 2006 semester. The E&M is looking a bit long, but doable. Mechanics is going to be just redoing old problems, but using the Hamiltonian method. I think it is going to be alright. Quantum Mechanics final on Tuesday! I am leaving tomorrow afternoon to Massachusetts for some quality time.
Snow is around the corner!
On Sunday I worked on the Classical Electrodynamics homework assignments. We are not studying electromagnetic waves. Most of the problems were about calculating transmission and reflected coefficients with two interfaces of materials. These problems have an awful amount of algebra with the boundary conditions. It was sad that I was not able to worked out all the cases for the last problem. Oh well! I am doing pretty bad on this course, so I have a feeling I am going to have to repeat it next fall, which is a bit annoying considering that I have to catch up on some fancy Theories...
After I handed the E&M problem set on Monday, it was time for Quantum Mechanics. Three problems, mostly on electromagnetic terms in the wavefunction (gauge invariance). The first one was about a magnetic monopole. The second problem was about the spin precession of an electron in a uniform magnetic field and the last problem was to calculate a commutator for the x- and y- components of the mechanical momentum. This problem set took a while since I was just out of it thinking of crazy things that were not helping. I handed the quantum problems today.
Finally Classical Mechanics! This time it was on fluid dynamics. Two problems, one to determine the free shape of a fluid rotating in a cylindrical vessel. The other was to find the velocity profile for a sphere submerge in a flowing fluid with constant asymptotic behavior. Fun, fun!
Two homeworks left for this fall 2006 semester. The E&M is looking a bit long, but doable. Mechanics is going to be just redoing old problems, but using the Hamiltonian method. I think it is going to be alright. Quantum Mechanics final on Tuesday! I am leaving tomorrow afternoon to Massachusetts for some quality time.
Snow is around the corner!
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