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====== Calculating the $S^{2}$ Matrix ======

===== The Prompt =====

**Using matrix notation, calculate** $S^{2}$**, when**

$$
S^{2}=S_{x}^{2}+S_{y}^{2}+S_{z}^{2}
$$

===== Context =====

This [[strategy:smallwhiteboard:|SWBQ]] is a great introduction to the S-squared operator and prepares students to think about this operator in the spin-1 system.  Students are often surprised to see that after factoring out constant terms, $S_{x}^{2}$, $S_{y}^{2}$, and $S_{z}^{2}$ each become the identity matrix.  The resulting constant term $\frac{3}{4}\hbar^{2}$ left over after adding the squared operators can also then be compared to the $l(l+1)\hbar^{2}$ term that most students have previously seen at some point. FIXME - Extra Information

===== Wrap Up =====

{{swbq:spsw:spswssquaredmatrix.ppt|Powerpoint slide}}
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{{swbq:spsw:spswssquaredmatrix.pdf|PDF slide}}

 



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