Chapter 8, Problem 43E

The Slater determinant is introduced in Exercise 42. Show that if states n and n’ of the infinite well are occupied and both spins are up, the Slater determinant yields the antisymmetricmultiparticle state:

${\psi }_n\left(x_1\right)\uparrow {\psi }_{n^{\prime }}\left(x_2\right)\uparrow {\psi }_{n^{\prime }}\left(x_1\right)\uparrow {\psi }_n\left(x_2\right)\uparrow$