Dresden 2011 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 7: Poster I
A 7.9: Poster
Montag, 14. März 2011, 16:00–18:30, P1
Building mathematical foundations for time-dependent density functional theory — •Markus Penz1 and Michael Ruggenthaler2 — 1Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria — 2Department of Physics, Nanoscience Center, University of Jyväskylä, 40014 Jyväskylä, Finland
In this presentation we study the essential mathematical structures for a rigorous foundation of time-dependent density functional theory, a reformulation of many-body quantum mechanics where the wave function as a fundamental variable is replaced by the electronic density. We introduce a new fixed-point proof of the fundamental one-to-one correspondence between densities and external potentials. Our approach not only sharpens the Theorems of Runge and Gross and van Leeuwen, as no additional time regularity is needed, but also yields interesting restrictions on the density and leads to a problem-adapted set of external potentials.