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H.Question 2: Quantum Mechanics

1. Let a and b be any two vectors that commute with ☎ = îôx + ĵôy + kôz. Show that
(ĉ · ã) (ô · b) = (ã · b)î + iỡ · (ã× b).
2. Find the eigenvalues and eigenstates of the spin operator Ŝ of an electron in the direction
of a unit vector n = Ĵ cosa + k sin a that lies in the yz plane making an angle a with
the y-axis.

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