UNCERTAINTY RELATIONSHIPS IN MANY-BODY SYSTEMS

Rigorous relationships among radial and logarithmic expectation values of an N-body system are obtained by means of information-theoretic methods. Especially interesting are the uncertainty expressions in terms of the product [r(alpha)](1/alpha)[p(beta)](1/beta), which generalize the well known relation [r(2)][p(2)] greater than or equal to 9N(2)/4. Additionally, an inequality involving the uncertainty in the logarithmic radius and the logarithmic momentum is shown. For illustration, the accuracy of the inequalities found are numerically analysed in a Hartree-Fock framework for atomic systems. Finally, it is pointed out how these inequalities are improved in atoms by taking into account other physical quantities or by considering some semiempirical results on atomic information entropies.