The Slater determinant is introduced in Exercise 42. Show that if states n and n' of the infinite well are occupied, with the particle in state n being spin up and the one in n' being spin down, then the Slater determinant yields the antisymmetric multiparticle state:
Ψn (x1) ↑ Ψn(x2) ↓ - Ψn (x1) ↓ Ψn(x2) ↑
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