Equation (9.1.14) seems to contradict (9.1.4), since it has a minus sign. Equation (9.1.14) is an equation for the density matrix elements, however, while (9.1.4) is for the time-dependent operator. Show that these two equations both give the same result for the time evolution of the element ρmn = c^∗_mc_n by explicit substitution, using |ψ_m⟩ = b^†_m|0⟩ and

= Ebbi |v) = qb|0). (9.1.18)