splamorprecession.ppt (Slides 1-3)

• Start by going through the expectation values of $S_{z}$, $S_{x}$, and $S_{y}$ for a general time-dependent state with the class. In particular, point out that the expectation of the z-operator has no time dependence while the x and y-operators do.
• The third slide has the expectation value of the general spin operator $\vec{S}$, which is composed of the expectation values of the x,y, and z spin operators. Remind students you can't make all of the measurements at the same time, but you can do a large amount of experiments and then combine the expectation values afterwards. This is perfectly fine.
• Introduce Ehrenfest's Theorem to the class. Ehrenfest's Theorem states that if you write any classical law for quantum mechanics in terms of expectation values, it will still be true.
• This theorem is partially why we commonly see crossover between quantum mechanics and classical mechanics.