A numerical study of the Lieb-Thirring kinetic energy lower bound

Abstract

In this work, the Lieb-Thirring kinetic energy bound is numerically examined for a variety of systems: the hydrogen-like atoms, neutral atoms, isoelectronic series of atomic ions, the Hooke's atom and some small molecules. For all of them, the accurate values of the kinetic energy and electron densities were used to find the best value of the constant C in the Lieb-Thirring bound. It is found that there is a lot of space to improve the bound and the Lieb conjecture, that the Thomas-Fermi constant is a good bound is numerically validated.