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So what did everyone think of the test? I thought the length was pretty good. I didn't, however, know what to do on problem 1 and am thinking that most people did get this one. I just didn't know what to do to show that it was an eigenfunction. Anyway I don't feel too bad about it because of the 20 point bonus that I think I got on the last problem. How'd everyone else fair?
I skipped over problem 1 twice before I realized I needed to consider <math>L</math>, <math>L_x</math>, <math>L_y</math>, <math>L_z</math> in spherical coordinates. With <math>\hat\phi=sin\phi-cos\phi</math> and <math>L_z</math> is the only one that commutes with <math>exp{im\phi}</math>. Or something to that effect. I'm sure I botched the proof on my exam so hopefully I get good partial too.
I just showed that operating <math>L_{z}</math> on <math>\psi</math> was equivalent to multiply <math>\psi</math> by a constant <math>\lambda</math>.
I did the same as chavez on the first question. It seemed a little too simple conceptually, so I hope that's what the question was asking… Does anybody think they did #3 correctly? That was a good problem, but I don't think I could do it even now without referencing the book a few times like with homework.
While I was doing the problem I thought I was doing it correctly. I won't really be able to know for sure until the scores come back, but it looked like you just take the 1x 1/2 table to … I forget the values now… and find the wavefunction by adding the probabilities of the separate solutions together. Then square it for the probability wavefunction. I definitely could be wrong though.
I thought #2 was fine, but I'm looking forward to checking out the solutions to #1 and #3. I'm not sure about the correct way to include <math>Y_l+m</math> correctly.
I'm not sure how many students understood the questions from the quiz correctly but based on these opinions above, it was difficult to understand the questions correctly for me either. I'm just worried how to prepare the final exam.
I am pretty sure Chavez and Zeno have it right - it's the definition of an eigenvalue, after all. What I did was convert the WF from polar to Cartesian coordinates, then operate <math>xp_y-yp_x</math> on it. You should then get a result that is a constant multiplied by the Cartesian form of the WF found earlier.
What is the coverage for final exam? Does it include all chapters which we've learned until now?
Looks like that's the plan.
From what Yuichi said, the test will cover Ch. 1-4 and 6. Apparently, we shouldn't expect anything from Ch. 5 since we really did not do anything with that section.