Inequalities among atomic expectation values

摘要

Some new inequalities involving various lang;rnrang; and lang;pnrang; atomic expectation values have been derived using theorems by Poacute;lya and Szegouml;. Using these inequalities, bounds on one expectation value can be obtained in terms of other expectation values. These bounds have been tested numerically using expectation values computed with wave functions of varying quality. Bounds obtained using Hartreendash;Fock and correlated wave functions are found to be fairly tight for small atomic systems considered. However, those obtained for neutral Thomasndash;Fermi atoms are not close to the correct Thomasndash;Fermi expectation values. The inequalities discussed here form a basis for obtaining bounds on unknown expectation values using known values of related expectation values.