Abstract
We construct for the Schrödinger operator in the semi-classical limit compact perturbations of a radial symmetric potential which give rise to resonances associated to arbitrarily high order poles for the meromorphic extension of the resolvent. Our results concern the hamiltonianP 0=−h 2Δ−x 2 in the 2-dimensional case, as well as a fairly large class of radial-symmetric potentials in the 3-dimensional case. We show that the poles of the resolvent for such a potential are necessarily simple, and subsequently the degeneracy is due to a lack of symmetry.
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Communicated by B. Simon
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Kaidi, N., Rouleux, M. Multiple resonances in the semi-classical limit. Commun.Math. Phys. 133, 617–634 (1990). https://doi.org/10.1007/BF02097011
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DOI: https://doi.org/10.1007/BF02097011