Bonn 2010 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 8: Quantum Mechanics
MP 8.2: Vortrag
Mittwoch, 17. März 2010, 15:25–15:50, JUR H
Regularity of Eigenstates in Regular Mourre-Theory — Jacob Møller1 and •Matthias Westrich1,2 — 1Dept. of Mathematics, University of Aarhus, Denmark — 2Institut für Mathematik, Johannes-Gutenberg Universität Mainz, Deutschland
Our presentation gives an abstract method for proving that eigenstates of a self-adjoint operator H lie in the domain of the conjugate operator A. Conjugation means here that H and A have a positive commutator in the sense of Mourre. The only requirement is the Ck-regularity of H.
Regarding integer k, our result is optimal. Using this method, we obtain cutoff-independent bounds and under a boundedness assumption of the multiple commutators we prove analyticity of the eigenstates with respect to exp(−itA).
We illustrate the relevance of this method in a physical application.