Trace formula and Levinson’s theorem as an index pairing in the presence of resonances
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Published:2024-08-02
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ISSN:0129-055X
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Container-title:Reviews in Mathematical Physics
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language:en
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Short-container-title:Rev. Math. Phys.
Affiliation:
1. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, Australia
Abstract
We realize the number of bound states of a Schrödinger operator on [Formula: see text] as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-energy corrections to find representatives of the [Formula: see text]-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients.
Funder
Australian Research Council
Publisher
World Scientific Pub Co Pte Ltd