{{page>wiki:headers:hheader}} %% Instructions: %% 1. Replace "The Question" with the question. %% 2. Change qmswzzz everywhere (2x) to the basename of this file. %% 3. Upload the PDF and PPT versions of the question. %% (Make sure to use the same basename.) %% 4. Change xx in the 2-letter acronym in the course footer to reference %% the correct course. %% 5. Delete these instructions when done! ====== 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}} \\\\ {{swbq:spsw:spswssquaredmatrix.pdf|PDF slide}} {{page>wiki:footers:courses:spfooter}} {{page>wiki:footers:topics:qmfooter}}