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The $S_{z}$ Operator


“Write down what you think the $S_{z}$ operator is in matrix form.”


This SWBQ offers students a chance to guess the $S_{z}$ operator and learn the process of how to find the $S$ operators in each orientation. Although students typically know that the $z$-oriented Stern-Gerlach experiment is directly related to the $S_{z}$ operator and that the result from a measurement is $\pm \frac{\hbar}{2}$, most may not know that these facts directly translate into matrix form.
Of course, this SWBQ is most beneficial if used before students have seen matrix forms of quantum operators. Additionally, this prompt is considerably more valuable if given before students have had the chance to fully internalize how measurements convert to mathematics.

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