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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Quantum Mechanics

MP 1.2: Vortrag

Dienstag, 16. März 2010, 08:55–09:20, JUR H

Lower bounds for atomic ground state energies via the Feynman-Kac formula — •Hans Konrad Knörr¹ and Hajo Leschke² — ¹Universität Mainz, Germany — ²Universität Erlangen, Germany

We consider a system of an atomic nucleus and electrons which are coupled by a pure Coulomb interaction. The ground state energy of this system can be calculated as a low temperature limit of a term that is written as a (conditioned) Wiener integral via the Feynman-Kac formula. Using this as a starting point we follow an idea of A. Debiard and B. Gaveau (Math. Phys. An. Geom. 3, 91-100 (2000)) to derive a lower bound to the energy spectrum. The supremum of the integrand of the Wiener intergral can be estimated by applying some methods from Stochastic Analysis, e.g. the Birkhoff-Chintchine ergodic theorem. The obtained lower bound to the ground state energy is very precise for small electron numbers.