Hartree-Fock Equations with a Perturbing Field

The Hartree-Fock equations under the action of an arbitrary field for any order of perturbation are set up in an integro-differential form. This form appears particularly advantageous for practical computation in such problems as electronic polarizability and electronic structure perturbations caused by nuclear moments. The equations are explicitly written down for a uniform perturbing field and a comparison is made with previous formulations. A wide variety of other applications is also discussed.