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===== Outcomes using successive Stern Gerlach devices (Lecture, 40 minutes) =====
{{courses:lecture:splec:spins_unit_sg_experiment.ppt}} Page 12-19

  * 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.

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