===== Dec 16 (Wed) last day! =====
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==== Can 12/16 ====
Can someone explain how to understand what the 4th quiz was asking for, such as problem 2 about <math>L_+</math> or <math>S_+</math>?
I am not asking how to solve the problem, just wondering generally how do you understand what the question was asking. This might seemed to be a silly question to ask, but it has bothered me a long time already this semester.


===John Galt 12/16===

Hey there Can. I think all it was asking, in simple terms, was to see the effect on the Z component of angular momentum if you mess around with the x and y components...

===prest121 12/16 5:45pm===
In HW problem 4.18, we were given this expression:

<math> L_\pm f^m_l = (A^m_l)f^{m\pm1}_l</math>

We wanted to solve for <math> A^m_l</math>.  We did this by using <math> <f^m_l | L_\mp L_\pm f^m_l> = <f^m_l | (L^2 - L^2_z \mp \hbar L_z)f^m_l> </math>

Eventually we got <math> \hbar^2 [l(l+1)-m(m\pm1)] = |A^m_l|^2 </math>

We can see that the solution of this can be <math>A^m_l = \sqrt{(l\mp m)(l\pm m + 1)}</math>, as we have in the book.  But other solutions are just as correct:

<math>A^m_l = -\sqrt{(l\mp m)(l\pm m + 1)}</math> or <math>A^m_l = \pm i\sqrt{(l\mp m)(l\pm m + 1)}</math>.

If we used any of these other versions, our matrices for <math>S_\pm</math> would be different, and thus, our matrices for <math>S_x</math> and <math>S_y</math> would also be different, since <math>S_x = (S_+ + S_-)/2</math> and <math>S_y = (S_+ - S_-)/(2i)</math>.

After all this, the question is whether or not this would change a certain fundamental QM relation of your choice.  Personally, I chose to see whether <math>S^2</math> was affected (it wasn't).


====John Galt 12/16====

If anyone who killed their tests sees this, would you mind bringing them to class today? I'm not sure if Yuichi is going to give us solutions to the previous exams, but they would be good review for the final. I could certainly use some help on test one and 3.

=== Yuichi ===
Solutions have been posted. Nevertheless, you can come to talk with me tomorrow (Friday).

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