Inequalities among atomic expectation values

Some new inequalities involving various 〈rn〉 and 〈pn〉 atomic expectation values have been derived using theorems by Pólya and Szegö. 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 Hartree–Fock and correlated wave functions are found to be fairly tight for small atomic systems considered. However, those obtained for neutral Thomas–Fermi atoms are not close to the correct Thomas–Fermi expectation values. The inequalities discussed here form a basis for obtaining bounds on unknown expectation values using known values of related expectation values.