(a) for a function f() that can be expanded in a taylor series, show that where p is an arbitrary angle. for this reason, lz/h is called the generator of rotations about the z axis. hint: use eq. (4.129) and refer to problem 3.39 more generally, l n/h is the generator of rotations about the direction n, in the sense that explil-mp/h] produces a rotation of the angle in the right- hand sense about the n axis. for spins, the generator of rotations is s·n/h in particular, for spin 1/2, tells us how spinors rotate (b) construct the 2 × 2 matrix representing a rotation by 180° about the x-axis and show that it converts "spin up" (x+ into "spin down" ( as one would expect classically (c). construct the matrix representing a rotation by 90° about the y-axis, and check what it does to x+. (d). construct the matrix representing a rotation by 360° about the z-axis. if the answer is not exactly what you would have expected, discuss its implications (e). show that e'(a-n)v/2 cosp/2 ) + i(σ . n) sin(p/2) - cos