Hence, there is always a basis for the eigenvalues of X where the action of P on any wavefunction is known: P ∫ ∫ x ψ ψ ( x ) | x ⟩ ⟩ = ∫ ∫ x − − i ψ ψ ′ ( x ) | x ⟩ ⟩ , and the Hamiltonian in this basis is a linear differential operator on the state-vector components, [ P 2 2 m + V ( X ) ] ∫ ∫ x ψ ψ x | x ⟩ ⟩ = ∫ ∫ x [ − − 1 2 m ∂ ∂ 2 ∂ ∂ x 2 + V ( x ) ] ψ ψ x | x ⟩ ⟩