At this point, we can hypothesize that the **operators that create fermion states do not commute**.
In fact, if we assume that the **operators creating fermion states anti-commute** (as do the Pauli matrices),
then we can show that fermion states are antisymmetric under interchange.
Assume
and
are the creation and annihilation operators for fermions and that they anti-commute.
The **states are then antisymmetric under interchange** of pairs of fermions.

Its not hard to show that the **occupation number for fermion states is either zero or one**.

Jim Branson
2013-04-22