Density matrix ρ̂

ρ̂ = Σ p_i |ψ_i⟩⟨ψ_i|: unifies pure and mixed states. Expectation ⟨A⟩ = Tr(ρ̂ A), evolution iℏ ∂_t ρ̂ = [H, ρ̂] (von Neumann).