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.