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Abstract
By means of a variational procedure the authors find a lower bound to the Thomas-Fermi kinetic energy of a fermionic system in the ground state, in terms of the moments (r-2), (r-1) of the fermionic density rho (r), and the number of particles, N, given by a formula which improves previous results. This expression allows them to bound the exact kinetic energy of a fermionic system by using the works of Lieb and Thirring. This variational technique can also be applied in order to bound density-dependent quantities of atoms as the exchange energy in Dirac's form and the average electron radial ( rho ) and momentum ( gamma ) densities, numerical and asymptotically because in these cases it is not possible to find exact analytical solutions.
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