Second Quantization

In 1928, P. Jordan and E.P. Wigner proposed the “second quantization” for electron wave functions by introducing the “anticommutation relations” $${b_{r}, b}$$ where b
†
r
and br are the creation and annihilation operators:
b
†
r
|0 >= |1r > and br|0 >= 0, (2)
with r denoting the relevant quantum numbers for a given particle. Show that
this formulation satisfies the Pauli exclusion principle. You can introduce the
occupation number operator Nr = b
†
r
br, if desirable.