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.