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!
20 November 2006
Nima Arkani-Hamed on Naturalness
On November 14th, Nima Arkani-Hamed gave a talk titled Naturalness, the String Theory Landscape and the LHC.
By now I have forgotten most of the details of the talk, so below is a sketch of the small amount of notes that I took.
--
The first part was to mention that the LHC will explore the weak energy scale. This energy scale is around 1 TeV. The weak scale is many orders above the Planck scale and many orders bellow the Hubble scale. This is part of the so-call Hierarchy problem.
This large leap make an "unnatural" fine tuning to 1 in 10^(-120) figures (in what I think is the cosmological constant, but I clearly suck at taking notes). Nima also mentioned that if you put a bunch of theoretical physicist in a spaceship, they will probably discover the Standard Model, with the right physics but all the numbers wrong.
An experimentalist fine-tunes a metal for example. (But I forgot the analogy here... :-( ).
Naturalness = compute until things blow in your face. For the weak scale to be natural, there should be some cutoff at 1 TeV. The LHC will run with 14 TeV in center of mass energy.
Nima then goes on to tell the story of the classical electron and the observation of the positron. Composite objects generate a doubling in degrees of freedom. For the weak scale there are two broad ideas:
An example of fine tuning is the nearly perfect alignment of the sun and the moon during an eclipse. The moon is the right size to cover the sun perfectly and leave a white halo.
The acceleration of the universe would be another finely-tuned aspect of the universe. If this were not the case, no structures would have ever formed. God? Other mechanism? Our planet is where structure is, around nebulae.
He then went on to talk about other universes, and looking for them. He also commented on split supersymmetry, but at this point I was already day dreaming. :-[
By now I have forgotten most of the details of the talk, so below is a sketch of the small amount of notes that I took.
--
The first part was to mention that the LHC will explore the weak energy scale. This energy scale is around 1 TeV. The weak scale is many orders above the Planck scale and many orders bellow the Hubble scale. This is part of the so-call Hierarchy problem.
This large leap make an "unnatural" fine tuning to 1 in 10^(-120) figures (in what I think is the cosmological constant, but I clearly suck at taking notes). Nima also mentioned that if you put a bunch of theoretical physicist in a spaceship, they will probably discover the Standard Model, with the right physics but all the numbers wrong.
An experimentalist fine-tunes a metal for example. (But I forgot the analogy here... :-( ).
Naturalness = compute until things blow in your face. For the weak scale to be natural, there should be some cutoff at 1 TeV. The LHC will run with 14 TeV in center of mass energy.
Nima then goes on to tell the story of the classical electron and the observation of the positron. Composite objects generate a doubling in degrees of freedom. For the weak scale there are two broad ideas:
- Supersymmetry (SUSY) - Bosons related to fermions, couplings related. This phenomena should show up at the TeV scale.
- Composites (Higgs made of techniquarks) - New dynamics.
An example of fine tuning is the nearly perfect alignment of the sun and the moon during an eclipse. The moon is the right size to cover the sun perfectly and leave a white halo.
The acceleration of the universe would be another finely-tuned aspect of the universe. If this were not the case, no structures would have ever formed. God? Other mechanism? Our planet is where structure is, around nebulae.
He then went on to talk about other universes, and looking for them. He also commented on split supersymmetry, but at this point I was already day dreaming. :-[
19 November 2006
The end is approaching!
The world is not ending! On the contrary is getting better.
What is approaching is the end of the semester! Eeee! The first semester of graduate school. It was something to me, something very, very frustrating. But I have learned a lot. Sadly I have learned the hard way, by committing crucial mistakes in homeworks and bad judgments. Some mistake include algebra and arithmetic mistakes ;-) . Other were volunteering to help type the string theory lecture notes with three core course, two lab sections, a seminar and a colloquium in my schedule. Oh well!
Tomorrow is my last "real" midterm. It is on Classical Mechanics: couple oscillations, 2-d motion including central forces and scattering, rigid bodies and rotations. Fun, fun! I have not studied that much, meaning that i have re-read the lecture notes and homework model solutions, but besides that not much. I think I could have prepare more, but I just want to get over with. A soft voice in the back of my head says Oh Mel! If you really want to get over with this, you should do better so you need not repeat the courses and waste more time! That might be true. But it is to late for that. I feel prepared (just like I felt the night before the Electrodynamics second midterm), and I hope I can at least understand the problems and work a great part of them in the test (unlike the Electrodynamics second midterm :-(). Then I will be relatively free, with some homeworks due on the week after Thanksgiving. I guess the "final" exam for Quantum Mechanics is on the last week of classes. I am really happy it is going to be a midterm-like test. :-)
What is approaching is the end of the semester! Eeee! The first semester of graduate school. It was something to me, something very, very frustrating. But I have learned a lot. Sadly I have learned the hard way, by committing crucial mistakes in homeworks and bad judgments. Some mistake include algebra and arithmetic mistakes ;-) . Other were volunteering to help type the string theory lecture notes with three core course, two lab sections, a seminar and a colloquium in my schedule. Oh well!
Tomorrow is my last "real" midterm. It is on Classical Mechanics: couple oscillations, 2-d motion including central forces and scattering, rigid bodies and rotations. Fun, fun! I have not studied that much, meaning that i have re-read the lecture notes and homework model solutions, but besides that not much. I think I could have prepare more, but I just want to get over with. A soft voice in the back of my head says Oh Mel! If you really want to get over with this, you should do better so you need not repeat the courses and waste more time! That might be true. But it is to late for that. I feel prepared (just like I felt the night before the Electrodynamics second midterm), and I hope I can at least understand the problems and work a great part of them in the test (unlike the Electrodynamics second midterm :-(). Then I will be relatively free, with some homeworks due on the week after Thanksgiving. I guess the "final" exam for Quantum Mechanics is on the last week of classes. I am really happy it is going to be a midterm-like test. :-)
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