(3) Angular distribution functions: (a) Sketch the polar plot of the directional dependence of the one-electron atom probability density for l = 2, and m₁ = 0. (b) At what angle 0 does the angular probability density have its minimum value? (c) Where does the angular probability density have a value one-fourth its maximum value? (4) Matrix Representation of Angular Momentum Operators: Consider the three states of l, and me: |l, me) → |1,1), |1,0), and [1,-1). Suppose we adopt a matrix representation and represent these three states by the three column vectors: 00-0 and The operators Lx, Ly, L₂, L+, L_ and [² will then be represented by 3 × 3 matrices. (a) Construct each of these matrices. (I'm so mean... sorry). (b) By explicit multiplication verify that [Lx, Ly] = ihLz.