Return to the experiment they did in lab 1 with two successive Stern Gerlach devices. Use this simple experiment to build their use of the state vector notation. They should see that if |+> goes into the analyzer, only |+> will come out of the analyzer. (slide 12)
Look at the experiment in slide 13 where the magnetic field is aligned along different directions. Here they should know from lab 1 that the probabilities are 1/2 and 1/2 out of the analyzer.
have them do the small whiteboard activity to determine a possible way to write the state |+>x in terms of |+> and |- >
use what was produced on the small white boards to show that there are multiple possible ways to obtain the probability of 1/2. With this as motivation, give the conventional definitions of the state vectors in x and y in terms of the state vectors along z (|+> and |- >).
Remind them of the postulate that shows how to find probability and test this formalism to show a simple probability calculation.
Then do the experiment on slide 14 which gives the unexpected result that even though all atoms start in |+>, they don't all end up in |+>.
Have students explicitly do the calculation for the probabilities to show that this result is consistent with the mathematical formalism they are developing.
Bring in polarizing sheets to show that crossed polarizers with a third sheet at an angle in between behaves exactly the same way. Emphasize that this result is not 'odd' - in fact the optical situation they likely saw in introductory physics is a direct analog to the quantum system.
Remind students of the 6 main postulates and show that we know now how to use 1 and 3, and have found them to consistently explain results that at first seem unusual.
Have students do the small group activity on state formalism
I used this point in the course as an opportunity to re-visit the fact that everything we are discussing and doing with the simulation is concrete and describes a real physical experiment.