Summary

• Have been considering spins as classical objects. Easy to visualize.

• Are really observing protons. Normally think of protons of as very quantum mechanical objects, with discrete states and limited number of observables.

• Want to remedy apparent discrepancies between these two descriptions of spin physics.

• Will provide motivation for NMR of other nuclei, and things to consider.

• Not going to re-do quantum mechanics in an hour. Do need to remember or accept that in quantum mechanics things exist in discrete states, and calculate things associated with the states like energy and angular momentum. Often observe that if you sum a large number of quantum states, get continuous distributions that we observe as classical systems.