Abeam of ag atoms, each with spin-1/2, is prepared in a way that 60% of the atoms are in the sz = +ħ/2 eigenstate of sz, and 40% are in the eigenstate sx = -ħ/2 of sc. (a) obtain the density matrix at t = 0, in the basis of eigenstates of sz. (b) admit that the atoms are subjected to a magnetic field b = boû, so that the hamiltonian reads, h = us. b (u is the magnetic moment of an atom). obtain the density matrix at time t, in the basis of eigenstates of sz. (c) calculate (sz) at times t = 0 and t.