Density matrix If a system is in state with probability pi and in stateψ2〉with probability p2,then the system is in a mixed state. The mixed state is represented as a density matrix p=p1lψ1)1|+p2lψ2)Kψ2l. ·In general,,if a system is in stateψi〉with probability pi,then the mixed state is p=∑ipilwi)ψil ·For pure state),p=lψ)Kψ.Density matrix • If a system is in state 𝜓1 with probability 𝑝1, and in state 𝜓2 with probability 𝑝2, then the system is in a mixed state. • The mixed state is represented as a density matrix 𝜌 = 𝑝1 𝜓1 𝜓1 + 𝑝2 𝜓2 𝜓2 . • In general, if a system is in state 𝜓𝑖 with probability 𝑝𝑖 , then the mixed state is 𝜌 = σ𝑖 𝑝𝑖 𝜓𝑖 𝜓𝑖 • For pure state 𝜓 , 𝜌 = 𝜓 𝜓