Time Independent Perturbation Theory: Nondegenerate Case, II

I'll start off by going back to the Two-State Problem. After attempting the homework problem on this, it makes a bit more sense, but not a lot. Basically Sakurai does perturbation using matrices. It still doesn't help me with the homework, though. Next Sakurai formally develops perturbation theory. He shows how to calculate the first order shift in the energy and the wavefunction. He then briefly does the higher orders. Next he renormalizes the wave-function, but I didn't understand this section at all. Basically, I don't understand Sakurai sometimes. This whole section is particularly dense. Then there are two examples.

I don't think I'll devote another post to the next section, which involves the degenerate case. Basically, you need to diagonalize the perturbation matrix. Only then will the degeneracy lift and you can solve the problem as in the non-degenerate case.

I think I will have to supplement with Townsend, discussion section, and banging through the homework as best I can. There is also Baym. Onward and upward.

Note to self: don't drink an entire bottle of wine (well, 2.5 glasses plus half a bottle) again. Even if you are preparing for your birthday. Perhaps you are not meant to drink to excess anymore. Blah. Yes I am writing this drunk. No, you can't really tell. Yay spelling and grammar! Or perhaps you can, because this is going to be rambling.

I watched An Inconvenient Truth the other night, and it was really good. I also watched Serenity, and that was really good as well. But back to Friday. If you haven't seen An Inconvenient Truth, you should. It makes me want to really put in the effort to reduce my carbon footprint. Sometimes I think I should be more involved in politics to do something and change things rather than be a physicist. I really hope that things change in November. I hope beyond hope that a democrat will win the presidency. I don't really care which one. I still need to decide who I want to vote for in the primary. I think if I don't vote for Kucinich I'll probably vote for Hillary. I still love the Clintons, and there's something about Obama that rubs me the wrong way. I don't know what it is. Part of me wants to be contrarian and get Hillary in the White House after Iowa. I don't think she could win the general election, however. No matter what, though, I'm ready for a change.

Also, while watching the movie, Al Gore talked about growing up on a tobacco farm. It made me wonder who thought smoking would be a good idea. How did the thought process work? "I wonder what will happen if I light these leaves on fire and inhale the smoke?" It's fascinating.

Time Independent Perturbation Theory: Nondegenerate Case

So Jordan Glassman has decided to keep a blog to help him understand Jackson. I am hoping that if I do the same for quantum mechanics it will improve my performance in the class. I understand the concepts when we go over them during lecture, but then I don't do well on the exams. So here we go. I'm starting with section 5.1 in Sakurai.

The problem is thus: there are very few cases where the Schrodinger equation can be solved directly. Here we have a Hamiltionian H=H₀ + V, where H₀ is a Hamiltonian that can be solved analytically and V is a small perturbation. This is generally written as H=H₀ + λV, so that we can expand the energy eigenvalues and eigenstates in powers of λ.

I do not understand the next section at all. It is called "The Two-State Problem." It looks Sakurai has the perturbation as a mixing term. Then Sakurai uses the analogy of the spin-orientation problem, but I don't think I read that section, so that's not helpful. He then ends with a convergence condition for the perturbation.

I am too tired to continue right now, so hopefully I'll write about the rest of the section tomorrow. Also, I should probably do the problem set and read Baym, as well.

Now back to your regularly scheduled brooding.

ARG

A girl I went to high school with has started her own business as a teen counselor/advice guru/whatever. It's all self-proclaimed anyway. We were in the same group of friends, but had a falling out in 7th grade and I refused to suck up to her so our relationship was never very close afterward. I think her blog is ridiculous and that parents who buy into her crap are stupid, but up until now she hasn't actually done anything that could be construed as harmful. This week, however, she decided to hand out medical advice on celiac disease, which she apparently has. I call bullshit on this, having known her for 6 years and never hearing her complain about feeling sick. If she truly did, I'm sure I would have heard about how she was sick all the time. This is the girl who had a wheelchair after having bunion surgery so she could get around school. Why she couldn't use crutches I don't know. Also, I think she's a pathological liar. She has no qualifications to even suggest this to people. Last I checked, a BA in Chinese and International Relations did in no way qualify one to practice medicine. I'm closer to having a doctorate than she will ever be, and mine will be a PhD in physics. Also, both my parents are doctors. Perhaps I should go into the field of giving bullshit advice, medical or otherwise. I'm sure I'd be 100 times better at it than she is.

She also makes a huge deal about smoking pot. She has many a blog post of letting parents know the signs their children are smoking, and also how she knows how bad it can be because she had many friends in high school that "ruined" their lives by smoking up. From what I remember, she used to regale us with stories of how badass her friends outside of Marlborough were because of all the crazy shit they did. She seemed almost proud. I do like how there are always comments along the lines of "You're a dumbass. Smoking pot isn't bad for you, etc."

Upon further thought, being a vegetarian is just not going to work out for me. I'll just work on reducing my meat intake, especially red meat, not that I eat it all that often. I just can't figure out what to eat for lunch if I'm a vegetarian, since lunch consists of sandwiches and I don't feel like eating peanut butter and jelly all the time.

New Year's Resolutions

1. Eat healthier. Eat less junk food (cookies, etc.) and eat more fruits and vegetables. I'm thinking of going as vegetarian as I can the majority of the time. I don't really cook meat, either, since I'm paranoid about it not cooking through all the way. The fish selection around here is pretty poor, also.
   
2. Exercise more. We'll see how this goes. Hopefully I will be able to go to the pool more often and swim laps.
   
3. Put more effort into my schoolwork and do better in my classes. Hopefully I will be able to manage both teaching and schoolwork so that I can join choir in the spring. They're doing Carmina Burana.
   
4. Stop pining over a boy. Find a new boy to pine for. Or get shit going with original boy.
   
5. Figure out who to work for.
   

The last one seems the most feasible.