Return to Q&A main page: Q_A
Q&A for the previous lecture: Q_A_1211
Q&A for the next lecture: Q_A_1216

If you want to see lecture notes, click lec_notes

Main class wiki page: home

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 could not think at all what to do for number one. What it was asking was so short and simple i just had no idea how to accomplish it.

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.

All you had to do for #1 was know that <math>L_z = -i\hbar \frac{\partial}{\partial\phi}</math>. Thus, <math>L_z\varphi = L_z(e^{i\phi}) = -i\hbar \frac{\partial}{\partial\phi}(e^{i\phi}) = \hbar(e^{i\phi}) = \hbar\varphi</math>. This is the definition of an eigenvalue.

I really liked problem 2. The fact that we could probe ANY quantum mechanincs relation made it really really simple. All i did was show that the eqigenstates of the spin matrices still were plus or minus hbar/2 and i got full credit.

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.

I remember him saying that as well–that the final covers 1-4 and 6.

is there ganna be a practice tests for final as well?

Is it all of 6? Or just some sections?

This kind of forum does not seem a good way to pin down this type of info. Misinformation seems to go around and around.

Setion 5.1 WILL BE included in the final, though 5.2 and later sections won't be.

Hyperfine structure will also be excluded from Chap. 6.

What is the meaning of “good” states coming from the first line of the discussion question?

I'm not entirely sure, but I think it means where the states are eigenfunctions of <math>J_z</math>, <math>L_z</math>, and <math>S_z</math>.

Think again.

i thought it meant states(combination of vectors) that will give you a diagonal matrix at the end instead of states that will have off-diagonal parts as well. not sure though!

Thanks, but I'm still confused. Based on your explanation, “good” states seems like to have only diagonal terms in the matrix. I thought that it has some relation with a balance of fine structure and zeeman effect.

Return to Q&A main page: Q_A
Q&A for the previous lecture: Q_A_1211
Q&A for the next lecture: Q_A_1216