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Bonn 2010 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quantum Mechanics

MP 8.2: Talk

Wednesday, March 17, 2010, 15:25–15:50, JUR H

Regularity of Eigenstates in Regular Mourre-TheoryJacob Møller1 and •Matthias Westrich1,21Dept. 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.

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