Open Access
January, 2011 Width of shape resonances for non globally analytic potentials
J. Math. Soc. Japan 63(1): 1-78 (January, 2011). DOI: 10.2969/jmsj/06310001


We consider the semiclassical Schrödinger operator with a well in an island potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of the result by Helffer and Sjöstrand [HeSj1] in the globally analytic case. We use an almost-analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions.


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Setsuro FUJIIÉ. Amina LAHMAR-BENBERNOU. André MARTINEZ. "Width of shape resonances for non globally analytic potentials." J. Math. Soc. Japan 63 (1) 1 - 78, January, 2011.


Published: January, 2011
First available in Project Euclid: 27 January 2011

zbMATH: 1210.81037
MathSciNet: MR2752432
Digital Object Identifier: 10.2969/jmsj/06310001

Primary: 81Q20
Secondary: 35C20 , 35P20 , 35P25

Keywords: microlocal analysis , quantum resonances , Schrodinger operator , semiclassical analysis , WKB constructions

Rights: Copyright © 2011 Mathematical Society of Japan

Vol.63 • No. 1 • January, 2011
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