with the resolution of the identity 1 = ∫ ∫ d x d p | x , p ⟩ ⟩ ⟨ ⟨ x , p | . Then, one obtains from equation (KvN algebra) ⟨ ⟨ x , p | λ λ ^ ^ x | Ψ Ψ ⟩ ⟩ = − − i ∂ ∂ ∂ ∂ x ⟨ ⟨ x , p | Ψ Ψ ⟩ ⟩ , ⟨ ⟨ x , p | λ λ ^ ^ p | Ψ Ψ ⟩ ⟩ = − − i ∂ ∂ ∂ ∂ p ⟨ ⟨ x , p | Ψ Ψ ⟩ ⟩ . Projecting equation (KvN dynamical eq) onto ⟨ ⟨ x , p | , we get the equation of motion for the KvN wave function in the xp-representation