===== Nov 30 (Mon)  =====
** Responsible party: Anaximenes, Dark Helmet ** 

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This lecture turned into mostly review.  I could use some help remembering specifically what we talked about.  I've put in the major topics below, and I'm working on adding the details.  If anyone can add something I've forgotten in the mean-time, that'd be great.

Major topics:
        *Brief discussion of Stern-Gerlach device
	*vector representation
	*First steps in adding angular momentum
		*including matrix representation
        *The last quiz will be on 12/11 instead of 12/04
        *continued the addition of angular momentum

As incorrectly stated in previous lecture:


<math>J^2 = \frac{1}{2}\hbar^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 2 & 0 \\ 0 & 2 & -1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math> 

What this should have said was 

<math>2(S_1)(S_2)= \frac{1}{2}\hbar^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 2 & 0 \\ 0 & 2 & -1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math> 

<math>J^2=(S_1+S_2)^2=(S_1)^2+(S_2)^2+2(S_1)(S_2)</math>

So we missed the <math>(S_1)^2</math> and <math>(S_2)^2</math> terms which bring:

<math>\frac{1}{2}\hbar^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math> 

which gives us the <math>J^2</math> matrix:

<math>J^2 = \frac{1}{2}\hbar^2 \begin{pmatrix} 4 & 0 & 0 & 0 \\ 0 & 2 & 3 & 0 \\ 0 & 3 & 2 & 0 \\ 0 & 0 & 0 & 4 \end{pmatrix} </math> 


We then found some of the Eigenvalues and Eigenstates of <math>2(S_1)(S_2)</math>

<math> \begin{pmatrix} 1-{\lambda} & 0 & 0 & 0 \\ 0 & -1-{\lambda} & 2 & 0 \\ 0 & 2 & -1-{\lambda} & 0 \\ 0 & 0 & 0 & 1-{\lambda} \end{pmatrix} </math> 

more will be coming when i figure out how to make arrows

 ((Please try to include the following

  * main points understood, and expand them - what is your understanding of what the points were.
    * expand these points by including many of the details the class discussed.
  * main points which are not clear.  - describe what you have understood and what the remain questions surrounding the point(s).
    * Other classmates can step in and clarify the points, and expand them. 
  * How the main points fit with the big picture of QM.  Or what is not clear about how today's points fit in in a big picture.
  * wonderful tricks which were used in the lecture.))\\
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