Calmness, finally

Things are finally settling down around here. Yesterday was my second statistical mechanics midterm: it was easy, but I am very disappointed at myself. I worked very slowly and only had time to work half of the first problem.

There were two problems. First we were given a 2-D electron ideal gas and were asked to find all thermodynamic characteristics for the case of zero temperature and temperatures very small compare to the Fermi energy. The other problem was to discuss an aparent contradiction with Bose-Einstein condensates. Below the critical temperature we know that the chemical potential is zero. This would imply that the Gibbs energy is zero. Generally the entropy of a system can be found by differentiation of the Gibbs energy with respect to temperature while fixing the volume and number of particles. Since the Gibbs energy is zero, then the entropy will also be zero. But in class the professor found an expression for the specific heat of the Bose gas as a function of temperature below the critical temperature. This specific heat can be integrated to yield the entropy, which in this case will be a non-trivial function of temperature. WTF?

I am disappointed at myself. I spent to much time organizing my thoughts during the test. First I quickly started calculating the energy and occupation number for the electron gas when the temperature was zero. Then I found the other potentials, but not the specific heats nor the entropy. All I found were things in terms of the area, surface tension and number of particles, so I could not take any derivatives, of course, since the temperature was fixed. It turns out that for any temperature you can calculate the number of particles in the system exactly since the integral can be evaluated analytically. But Melvin here just stared at the paper for a long time trying to remember how to integrate such things as one-over-e-to-the-x-plus-one.

In the end I do not think all the work I handed in is worth 50 points (out of the 100 points the first problem was worth). I did not even worked on the case for temperatures below the Fermi energy. I presume that some sort of series expansion was needed. I have realized that I am not good with series expansions and I need a lot of time to set everything up. This makes me very sad because I believe that being able to work with series expansions is very important for physics. I should settle down and learn them right once and for all, before this goes to far... if it does...

For the second problem I just wrote down some garbage on how I believe the Gibbs energy was not zero dealing with the fact that there are two phases present below the critical temperature (the condensate and the gas). Now that I think of it, well no. The entropy when the temperature tends to zero should tend to zero too. Also in phase equilibrium both phases have the same value for the chemical potential. Anyways, the whole point is that the test made me feel really stupid.

Yesterday at the electrodynamics recitation the professor stated the following problem. Consider a charged particle at rest in a region of constant electric and magnetic field, with the fields perpendicular to one another and having the same magnitude (in Gaussian units!). What is the trajectory of the particle?

We fiddled with the problem by writing down the Lorentz force law. Because of the Lorentz-gamma factor, the differential equations for the velocity or momentum components look kinda nasty. The professor believed that there was an analytical solution, but he said he was to lazy to find it so he would prefer to solve this problem numerically. This was just for fun, but I kept on thinking about it and decided to work on it during the night. I discretized the two equations and found a nice system of couple differential equations. It is not very complicated, but I just suck at debugging code, so it was not until this morning when I was able to make the program run properly. I found what was expected: the magnitude of the velocity tends to the speed of light, and the trajectory just blasts off to infinity with slight distortions. I felt happy, since I had accomplished something that appeared to be correct. So I emailed the professor some of my results and went to my class.

It turns out that the professor had found an analytical solution for this problem, so I seem not to pay much attention to my results. My ego was just demolished :-(.

And it has been like this during the past weeks. I am feeling like a forgotten piece of crap, very useless. On my previous SM midterm I got something like an 84 out of 150, on the QM midterm I did slightly better with 14.8 out of 20, the average being around 14 so I guess I am above average. But I have not been doing that well in the homeworks, there is alway a bloody problem where I do not have a bloody clue on what to do. A more positive picture is on EM where I was able to score a 95/100 in the midterm, and my homeworks are not that bad. But in SM... oh boy. Two homeworks ago we had to calculate the third virial coefficient for the hard-sphere model of a non-ideal gas. It was way more complicated than I thought, so I only got half credit. In fact, only two students got the correct result, most of the class got half-credit. Then on the previous homework we had to find an expression for the vapor pressure of the van der Waals model. Again, I did not worked this problem completely and expect to do very poorly. All this added to not doing well on this second midterm may imply that I could fail this class. Ahh!

I do not even want to think about it. Currently I have been over worried thinking about next semester. I am planning on taking Quantum Field Theory and Relativity and hopefully a breadth course. At the same time I should attend more theory seminars and maybe the Strings course.

Summer plans

My summer plans currently consist of just trying to absorb as much as possible from Srednicki's Quantum Field Theory and Frankel's The Geometry of Physics. I emailed some professors in the math department here in Stony Brook. My idea is that I do not have the background to work on a string-related project yet, but I could take a mathematics project. I know that I also do not have the mathematical background for a math project, but I figured it would be more effective for me to learn some math during the summer and in the end do some sort of calculation than learn some partial stuff with strings and then have to wait another year to continue. I still have to email some other professors... who knows!

Divergent Series (The Haunt of)

So one class ago my QM professor talked about how infinite series creep on you and sneak on you to come and blow up on your face if you do not truncate them, say like for the Hydrogen atom problem.

I guess these are what a theorist's nightmares are made off...

Srednicki's

Also, I got a copy of Srednicki's QFT textbook. Should be fun!

Before the tempest...

Well March is going to be hell month. Three midterms and a seminar presentation. I gave the seminar this past Wednesday. It went better than I expected, with not so many annoying questions. Next week starts the one-midterm-per-week with EM.

Sometimes one has to know when to stop. I have been struggling with a problem from SM. A two-level system, approaching it with the grand canonical distribution. I just cannot get anything to come out like the results from the canonical or micro canonical. Anyways, I am sick of it. Tomorrow I will check the library for other sources. Now I shall start with this week's EM homework, which finally has some problems on relativity ;-).

Wordpress

I am going to be doing some blogging over at Wordpress, since they have enable LaTeX typesetting! That is so cool! :-).

Destroyed

Phew! Just finished grading this week batch of lab reports. Last week saw my ego completely destroyed by the first midterm on statistical mechanics.

It was an easy exam. The first problem was a collection of two-level systems; we were asked to find thermodynamic quantities and analyze them. I started doing things the wrong way, until I finally realized I had to find the partition function and calculate everything from there. It was to late when I figure things out. The second problem was a rotating cylinder with a pressure in its axis, we were asked to find the pressure in the boundary. Again, I started walking the wrong path and by the time I realized what I had to do it was to late. Literally, time was up. So I handed in two less-than-half-way done problems.

I was angry at myself. So angry that during lunch I bit my own tongue. I hated myself for not thinking things right. Then I felt in this thinking storm of how I sucked as a physics student, how I was alright back in Puerto Rico and how I am never going to make it to work with quantum gravity. It made me feel really low. I went to Boston during that weekend and worked on homeworks.

I had worked on EM previously during the week, but on Sunday night I realized that what I did was very wrong. It turned out I only had solved correctly one problem, out of 4. Again, it made me feel so hopeless. I ended up arriving at Stony Brook around 8:30 PM to grade my part of the midterm grading for the class I am TAing. It turned out that the professor wanted the grades early, so he had started grading my part with another instructor. I felt so bad when I saw somebody doing my job. I graded a bit of what was left and helped entered all the grades to the spreadsheet in the computer. This lasted until 3:00 AM.

While walking back to my apartment I saw the snow falling down on the campus. That night and Monday we had like 3 inches of snow. I think most of it is melted now, since it had been relatively warm lately. On Tuesday I got my grade from the midterm and it was not that bad, 85/150. The average was around 100, so I am well below average. I do not feel that bad, because I know that (at the end) I had an idea on how to solved the problems.

I also email some professors in the mathematics department asking for summer research. Three out of four already replied with a negative answer, mostly the same; they are busy, they are going to be gone during the summer, they do not have anything to offer, and I can always take courses to learn. I get a bit annoyed by the fact that they tell me I can take the courses. While it is true, I can take the courses at some point, I also have to take a lot of other courses. I am tired of taking courses and solving textbook problems. I want to work with somebody, and to learn things in a non-linear way. Oh well, there is still one professor who has not replied, but I do not have my hopes high...

Still, I am a happy person.