Note on the variation step in the iteration-variation approach. Illustration on the hydrogen atom

An analysis of the analytical properties of the first iterate of the iteration–variation approach applied to small Gaussian expansions is reported in the case of the hydrogen atom. The first iterates embody important qualitative improvements such as a cusp near the origin and better asymptotic decay at large values of r. Actual values of the properties depend on the quality of the initial functions in such a way that for very small Gaussian expansions the variation step is necessary.