{{page>wiki:headers:hheader}}

===== Spin Precession (Lecture, XX minutes) =====
{{courses:lecture:splec: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

{{page>wiki:footers:courses:spfooter}}