Mathematisches Kolloquium

Zusammenfassung: Since the early times of quantum mechanics, there has been interest in estimating the energy of the electrons in an atom in terms of the single particle density of the electrons (i.e., the electronic density). The first such estimate was proposed independently by Thomas and Fermi in 1927. The interest here is to express the so called "indirect term" of the Coulomb repulsion of the electrons as a functional of the single particle density. This task was initiated by Dirac, in 1930. The first rigorous estimate was obtained by Elliott H. Lieb, in 1979. A later improvement was obtained by E. H. Lieb, and S. Oxford in 1981. The Lieb-Oxford bound is proportional to the integral of the four third power of the single particle density. Our result is an alternative to the Lieb-Oxford bound. We get a better constant to the expense of adding a sort of gradient term of the single particle density. This is joint work with G. Bley (PUC, Santiago) and M. Loss (Georgia Tech, Atlanta).

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