Solution
= Solution
If two <fermions> occupied the same complete <spin orbital> $u$, their antisymmetrized product would be
$$
\frac{u(1)u(2)-u(2)u(1)}{\sqrt2}=0.
$$
The zero vector cannot represent a normalized <quantum state>. This is the <Pauli exclusion principle>: at most one identical <fermion> occupies any complete one-particle state. Two <electrons> may occupy the same <spatial orbital> with opposite spins, because $a\alpha$ and $a\beta$ are different <spin orbitals>.