spins_unit_schrodinger_time_evolution.ppt Pages 12-35

• Remind students classically of why a magnetic moment will re-align in a magnetic field, and use that to motivate the appropriate Hamiltonian
• Derive the Hamiltonian for a static B-field along the z-axis for simplicity
• Remind students that this commutes with Sz, so we already know the stationary states (the eigenstates), and thus the basis set, and can thus write down all possible states directly
• Do a sample calculation showing how to use this to show our stationary states have time-independent probabilities, and our general mixed states have oscillatory probabilities
• Let students do probability calculations for this system in a short whiteboard activity
• Do longer whiteboard activity where students find the general spin vector S(t)
• Use the equation the students 'found' for S(t) to discuss spin precession - discuss how to interpret the equation for different values of theta and phi
• Go back to the classical prediction to show that this precession is not unexpected
• Introduce a similar set of calculations but for an arbitrarily aligned magnetic field
• Introduce Larmor frequency and spin flip
• (note) This is quite a bit of heavy calculations for the students at this phase - activities could be used to help them grasp this better.
• It is important to discuss with the students what 'spin space' is and how this is not a direct 1 to 1 mapping with 3-d real space. They should understand both what is different between this and the classical precession, but also not be confused by thinking it is a direct spatial mapping. I introduced some research papers and perspectives from experts on how to 'visualize' spin