(b) The first four spherical harmonics, Ym (0, 0), are given by YO = Y = = Y = == =X 1 4T =0 3 8 sin ei Y- = f(r) f(r)* rdr = 1 and i. By inspection (or calculation) express the wave function as a superposition of eigenstates of (where each may include the additional factor f(r)). [4] 3 4 3 8 ii. The wave function factors are separately normalised such that ro=2 0=T cos 100 100 37 sin e i sin 0 cos sin d0 d = 1. For each coefficient of your expansion, state the integral that could be evaluated to give that coefficient (but you do not need to calculate them). [3] iii. A measurement of L2 and the z-component, L, is made. State the possible value(s) that might be obtained for L. State the possible value(s) that might be obtained for L. Give the probability in each case. [3]