  This thesis is a multidisciplinary contribution to the information theory of
single-particle Coulomb systems in their relativistic and not relativistic
description, to the theory of special functions of mathematical physics with
the proposal and analysis of a new set of measures of spreading for orthogonal
polynomials, to quantum computation and learning devices and to the analysis of
entanglement in systems of identical fermions, in this field we propose a
separability criteria for pure states of N identical fermions and the
entanglement of two-electron atoms is studied, a new separability criteria for
continuous variable systems is also analyzed. The notions of information,
complexity and entanglement play a central role.
