• Point out to the class that the use of these kets looks a lot like a vector space. We don't know how many dimensions the vector space has, but we can assume that since the S.G. device has two outputs we are likely working in a 2-dimensional vector space.
• Draw a Stern-Gerlach experiment showing the spin down port of a z-oriented device going into a second z-oriented device. Write down on the board that the probability of particles leaving the second device in the states $\vert+\rangle$ and $\vert-\rangle$ are mathematically written as

$$\mathcal{P}_{+}=\left\vert\langle+\vert-\rangle\right\vert^{2}$$ and $$\mathcal{P}_{-}=\left\vert\langle-\vert-\rangle\right\vert^{2} \; \; , $$

respectively.