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I'm having a hard time describing the pace the class is going and, specifically, whether I like that pace. I don't really have any good questions to post to the wiki, and I think that's partially because I already understand the material we're going over (suggesting that we're going too slow) and partially because I haven't had time to go through the material in the book that we're not covering (suggesting that going faster might be too much). Going slower than necessary does have some advantages (once in a while, a minor philosophical point comes up that otherwise wouldn't have), but things often seem painfully slow.

How does everyone else feel about our pacing?

I think we slowed down a lot after the first quiz, a bit too slow for me. The Monday lecture, in particular, was basically a review. I suspect that Yuichi is trying to make sure we all have a certain baseline level of understanding of what we've done so far, so people don't get totally lost in chapter 4.

Yes, I am on the same page with Mr. Faraday here. Class has been interesting and I previously thought going slower might be better, but it would be interesting to at least try it out at a faster pace and see what we think then.

And immediately after writing up the question above, I found a question to ask. A student expressed in lecture that she could state the definition of Hilbert space from page 94 but didn't feel like she had a good intuitive understanding of it. For reference, that definition is the set of square-integrable functions on a specified interval,

<math>\displaystyle f(x) :: \int_a^b |f(x)|^2 dx < \infty </math>

We decided to leave the question alone and say that parroting the definition was enough. In footnote 25 on page 119, however, Griffiths states that this definition was already too restrictive because it was over x, specifying the “position basis” rather than some arbitrary basis. I think this brings the question up again. Is a vector that's in Hilbert space over one basis also in Hilbert space over all other bases (or at least the ones we can talk about in physics)? If so, how do we know? If not, what does it mean when Griffiths says that the vector “lives 'out there in Hilbert space' ” rather than with respect to a particular basis? I think that in light of this issue, it's reasonable again to ask for a better understanding of what it means to be inside (or outside) Hilbert space. What's a vector outside of Hilbert space–a vector with infinite magnitude?

I appreciate this question, and although I have no answer, would like to say I think I'd profit from exploring this more clearly in class as well.

I'm having some difficulty with the generalized uncertainty principle - not in understanding the mathematical derivation, but mainly the fact that it is a mathematical derivation. I realize that quantum mechanics itself is a mathematical construct, but it seems strange to me that the uncertainty principle falls out of our own mathematics and not some sort of physical law. Any thoughts?

Maybe it's just been a while since I took Linear Algebra and I'm just rusty on these matrix operations, but on page 121 of Griffiths, where does the determinate come from when they're looking for eigenvectors and eigenvalues of H, and why are they subtracting E?

I'm trying to make sense of how the different “spaces” are represented in short-hand. Correct me if I'm wrong!

Energy space <math>C_n</math> in short-hand is <math><f_n|\Psi></math>. (by equation [3.46])

Momentum space <math>\Phi(p,t)</math> in short-hand is <math><f_p|\Psi></math>. (by equation [3.53])

“Real” space <math>\Psi(x,t)</math> I'm not sure about. Is it simply: <math>|\Psi></math> or in terms of <math>\Phi</math> and equation [3.55] I get a short-hand of <math><f_p|<f_p|»</math>. Does that make any sense??

I just thought it would be <math><\Psi_n|\Psi></math>. Then again, I could be wrong.

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