Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
• One can visualize the quantized values of the spin angular momentum S with a semiclassical “vector model,” as described in Section 8.6 for the orbital angular momentum L. In particular, the quantization of Sz requires that the vector S must lie on certain cones, like the one sketched in Fig. 8.15. (a) Make a sketch similar to Fig. 8.14 showing the two possible orientations of S for an electron. (b) What is the angle between S and the z axis for these two states?
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