Maximum-entropy inference and momentum density approach

Previously, we have proposed a rigorous method to obtain the total energy E of a system of interacting atoms based on the electron momentum density and its redistribution during the interaction process. In this paper, we consider an inverse problem of constructing the momentum density distribution from the knowledge of the total energy E. Using the method of the maximum-entropy inference in information theory, analytical expressions are derived for the radial momentum density as a function of E. The results are applied to the interactions in the H2 system and the reliability of the inference is examined. In spite of its simplicity, the inferential momentum distribution is shown to be reliable semiquantitatively.