New Method for Constructing Solutions to Time-Dependent Perturbation Equations

Abstract

A method is developed for obtaining solutions to the usual first‐order perturbation equations arising from the presence of a harmonic perturbation. By means of piecewise polynomial approximations to the unperturbed potential and to the perturbation, the method yields the first‐order wavefunction in piecewise analytic form. It is easy to obtain error bounds to the relevant second‐order properties. The method can be extended to multidimensional problems or to problems involving nonlocal potentials. Numerical application is made to the calculation of the frequency dependent dipole polarizability of the hydrogen atom and of the helium atom within the uncoupled Hartree—Fock approximation.