Calculating the $S^{2}$ Matrix

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

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

This 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. - Extra Information

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