Perturbation Theory and the Hellmann—Feynman Theorem

By using the Hellmann—Feynman theorem in conjunction with an operator formulation of perturbation theory it is shown that, while for a general Hamiltonian an energy derivative is determined only to order n by an nth-order wavefunction (Salem and Wilson), for a restricted class of systems it is determined to order n+1, and by restricting the class somewhat further one can obtain energy derivatives to order 2n+1. The example of the force between two atoms interacting through dispersion type forces is briefly discussed.