Let în be a unit vector in a direction specified by the polar angles (0, ø). Show that the component of the angular momentum in the direction ân is 6.12 L, = sin0 cos pL, + sin0 sin øL,y + cos 0L: = } sin (e-* L, + e* L_) + cos 0 L̟. If the system is in simultaneous eigenstates of L² and L; belonging to the eigen- values I(I + 1)h² and mh, (a) what are the possible results of a measurement of L„? (b) what are the expectation values of L, and L?

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A: The solution is easy to see

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