The physical meaning of the non-commutativity can be understood by considering the effect of the commutator on position and momentum eigenstates. Let | ψ ψ ⟩ ⟩ be a right eigenstate of position with a constant eigenvalue x 0. By definition, this means that x ^ ^ | ψ ψ ⟩ ⟩ = x 0 | ψ ψ ⟩ ⟩ . Applying the commutator to | ψ ψ ⟩ ⟩ yields [ x ^ ^ , p ^ ^ ] | ψ ψ ⟩ ⟩ = ( x ^ ^ p ^ ^ − − p ^ ^ x ^ ^ ) | ψ ψ ⟩ ⟩ = ( x ^ ^ − − x 0 I ^ ^ ) p ^ ^ | ψ ψ ⟩ ⟩ = i ℏ ℏ | ψ ψ ⟩ ⟩ , where Î is the identity operator.