8. (14 points) Write down the Slater determinants (or linear combination of Slater determinants) for
(a) (8 points) the He atom at the lowest excited state in accord with Hund's rule with Ms = 0.
(b) (6 points) the Li atom in its ground state with Ms = -1/2.
9. (24 points) For a two electron system, (a) give all the electronic spin functions for the triplet state
and the singlet state; and (b) draw plots to show the orientations and the magnitude of the spin
vector S1, S2, and S (S = S1+S2) for both spin states of S= 1, Ms = 0 and S = 0, Ms = 0.
10. (12 points) For a hydrogen-like atom, give the results for the following operation on the spin-orbital
function: (a) L²(3d¹ß); (b) Lz(2p₂a); (c) S²(2sa); (d) $₂(3poß)