(a) Show that the time evolution of the density operator is given by
ρ^(t)=U^(t)ρ^(0)U^†(t)
where U^(t) is the time-evolution operator, namely
U^(t)∣ψ(0)⟩=∣ψ(t)⟩
(b) Suppose that an ensemble of particles is in a pure state at t=0. Show the ensemble cannot evolve into a mixed state as long as time evolution is governed by the Schr\"odinger equation.