Moreover, according to the operator axioms and (xp eigenvec), ⟨ ⟨ A ⟩ ⟩ = ⟨ ⟨ Ψ Ψ ( t ) | A ( x ^ ^ , p ^ ^ ) | Ψ Ψ ( t ) ⟩ ⟩ = ∫ ∫ d x d p ⟨ ⟨ Ψ Ψ ( t ) | x , p ⟩ ⟩ A ( x , p ) ⟨ ⟨ x , p | Ψ Ψ ( t ) ⟩ ⟩ = ∫ ∫ d x d p A ( x , p ) ⟨ ⟨ Ψ Ψ ( t ) | x , p ⟩ ⟩ ⟨ ⟨ x , p | Ψ Ψ ( t ) ⟩ ⟩ = ∫ ∫ d x d p A ( x , p ) ρ ρ ( x , p ; t ) . Therefore, the rule for calculating averages of observable A ( x , p ) in classical statistical mechanics has been recovered from the operator axioms with the additional assumption [ x ^ ^ , p ^ ^ ] = 0 . As a result, the phase of a classical wave function does not contribute to observable averages. Contrary to quantum mechanics, the phase of a KvN wave function is physically irrelevant. Hence, nonexistence of the double-slit experiment as well as Aharonov–Bohm effect is established in the KvN mechanics.