A lithium atom has three electrons. These occupy individual-particle states corresponding to the sets of four quantum numbers given by (n., ℓ, m ℓ, ms) = (1, 0, 0, +½), (1, 0, 0, -½), and = (2, 0, 0, +½), Using ψ 1.0.0 (rj) ↑, ψ 1.0.0 (rj), ↓ and ψ 2.0.0 (rj) ↑ to represent the individual-particle states when occupied by particle. j, apply the Slater determinant discussed in Exercise 42 to find an expression for an antisymmetric multiparticle state. Your answer should be sums of terms like
ψ 1.0.0 (r1) ↑ ψ 1.0.0 (r2) ↑ ψ 2.0.0 (r3) ↑
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