ELECTRON SPIN IN THE REPRESENTATION WHICH MAKES σ _z DIAGONAL AND IN THE REPRESENTATION THAT MAKES σ _x DIAGONAL

We calculate the density matrix of an electron spin in the representation that makes diagonal and hence calculate the ensemble average of the expectation value of .We make the same scheme in the representation that makes diagonal and show that the ensemble average of the expectation value of , resulting from this representation is precisely the same as the initial one, where are Pauli’s spin matrices and is the z-component of the intrinsic magnetic moment of the electron. We then conclude accordingly.