Deviations from spontaneous Lyman-alpha exponential decay revisited: A rigorous treatment within a two-level nonrelativistic model

A recent paper by Facchi and Pascazio, in which the advantage of numerical evaluations of deviations from exponential decay was pointed out, makes a r evisitation of the subject necessary. All the more, since the above-mention ed authors have not estimated the error bounds (being absolutely necessary in any calculation) for their results. On the contrary, the accuracy of all results presented in this paper is proved by error estimates. Moreover, fo r the first time, the power of the simple iteration method in calculating b oth the exponential and non-exponential time evolution of an unstable atomi c state is demonstrated.