The "dressed" states themselves can be derived, in first-order perturbation theory too, as ψ ψ n ′ = ψ ψ R , n + 1 2 ∑ ∑ k ≠ ≠ n ∑ ∑ j ψ ψ R , k V k j ′ V j n ′ 2 d j − − d k − − d n ( d j − − d n ) ( d j − − d k ) ( d n − − d k ) Notice the index R to the unperturbed eigenstate ψ ψ R of D 0 to recall the current rotated basis of H D . To express the eigenstates in the natural basis ψ ψ of H itself, it is necessary to perform the unitary transformation ψ ψ R → → U − − 1 ψ ψ .