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