Sur la theorie des equations de Hartree–Fock dependent du temps. V. Etude d'un modele spherique a 2 electrons. Calcul du tenseur d'hyperpolarisabilite d'ordre 3

In order to apply the TDHF equations in the matrix form we established previously, we conceive a model for which the static Hartree–Fock equations are rigorously solved; so we study problems only linked to the TDHF method, independent of any further approximation (for example, of LCAO type). This model is made of a spherical box containing electrons subject to a particular potential. We solve, numerically, the TDHF equations at different orders, and we calculate the third order hyperpolarizability tensor. We then compare our results with the ones given by a variation‐perturbation method.