[en] Two approximations of interest in atomic, molecular, and solid state physics are explored. First, a procedure for calculating an approximate Green's function for use in perturbation theory is derived. In lowest order it is shown to be equivalent to treating the contribution of the bound states of the unperturbed Hamiltonian exactly and representing the continuum contribution by plane waves orthogonalized to the bound states (OPW's). If the OPW approximation were inadequate, the procedure allows for systematic improvement of the approximation. For comparison purposes an exact but more limited procedure for performing second-order perturbation theory, one that involves solving an inhomogeneous differential equation, is also derived. Second, the Kohn-Sham many-electron formalism is discussed and formulae are derived and discussed for implementing perturbation theory within the formalism so as to find corrections to the total energy of a system through second order in the perturbation. Both approximations were used in the calculation of the polarizability of helium, neon, and argon. The calculation included direct and exchange effects by the Kohn-Sham method and full self-consistency was demanded. The results using the differential equation method yielded excellent agreement with the coupled Hartree-Fock results of others and with experiment. Moreover, the OPW approximation yielded satisfactory comparison with the results of calculation by the exact differential equation method. Finally, both approximations were used in the calculation of properties of hydrogen fluoride and methane. The appendix formulates a procedure using group theory and the internal coordinates of a molecular system to simplify the calculation of vibrational frequencies