4.7 Ways to Symmetrize the Wave Function

1

Can two electrons be in the spatial ground state of the same hydrogen atom?

2

Can three?

3

Can three spinless bosons?

4

If there are three identical fermions in three differents states $\psi_1$, $\psi_2$, and $\psi_3$, how does the wave function look?

5

If there are three identical fermions in four differents states $\psi_1$, $\psi_2$, $\psi_3$, and $\psi_4$, how many indeterminate coefficients does the wave function have after the antisymmetrization requirements have been enforced? (Hint: how many Slater determinants can you write down?)