1) Find the matrix form of the density operator using | :i: 2) as basis. 2) Find the matrix form of the density operator using | :i: m) as basis. 3) Find the ensemble average of oz. An ensemble of electrons are put inside a uniform magnetic field along the z-axis B = B2. The electron possesses a dipole moment which, in terms of the Pauli matrices, may be written as d = po. The Hamiltonian of the electron in the magnetic field is H = -d . B = -uBoz. At thermal equilibrium with temerature T, the ensemble can be described with the density operator p = e-BH /Tre-BH] with B=1/ (kBT)