Chapter 5.2, Problem 5.12P

(a)

To determine

A solution to a completely symmetric function and a completely antisymmetric function which also satisfy the Schrodinger equation with same energy and determine what happens to the completely antisymmetric function if $\psi \left(r_1,r_2,r_3,\mathrm{...}{r}_z\right)$ is symmetric in its first two arguments.

(b)

To determine

Show that a completely antisymmetric spin state for $Z$ electrons is impossible, if $Z>2$.