Semiclassical resolvent estimates for Schrödinger operators with Coulomb singularities

Knauf A, Castella F, Jecko T (2008)

Publication Type: Journal article, Original article

Publication year: 2008

Journal

Annales Henri Poincaré Institute Henri Poincaré

Publisher: Institute Henri Poincaré

Book Volume: 9

Pages Range: 775--815

Journal Issue: 4

DOI: 10.1007/s00023-008-0372-x

Abstract

Consider the Schrödinger operator with semiclassical parameter h, in the limit where h goes to zero. When the involved long-range potential is smooth, it is well known that the boundary values of the operator’s resolvent at a positive energy λ are bounded by O(h −1) if and only if the associated Hamilton flow is non-trapping at energy λ. In the present paper, we extend this result to the case where the potential may possess Coulomb singularities. Since the Hamilton flow then is not complete in general, our analysis requires the use of an appropriate regularization.

Authors with CRIS profile

Andreas Knauf Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

Université de Rennes 1 / University of Rennes 1 FR France (FR)

How to cite

APA:

Knauf, A., Castella, F., & Jecko, T. (2008). Semiclassical resolvent estimates for Schrödinger operators with Coulomb singularities. Annales Henri Poincaré, 9(4), 775--815. https://dx.doi.org/10.1007/s00023-008-0372-x

MLA:

Knauf, Andreas, François Castella, and Thierry Jecko. "Semiclassical resolvent estimates for Schrödinger operators with Coulomb singularities." Annales Henri Poincaré 9.4 (2008): 775--815.

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