Evaluate the density matrix ρmn of an electron spin in the representation which makes σ^x diagonal. Next, show that the value of ⟨σz⟩, resulting from this representation, is precisely the same as the one obtained in Sec. 5.3.
Hint: The representation needed here follows from the one used in Sec. 5.3 by carrying out a transformation with the help of the unitary operator
U^=(1/2−1/21/21/2).