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Trace formula and Levinson's theorem as an index pairing in the presence of resonances
Published 25 Feb 2024 in math.KT, math-ph, math.MP, and math.SP | (2402.15979v1)
Abstract: We realise the number of bound states of a Schr\"{o}dinger operator on $\mathbb{R}n$ as an index pairing in all dimensions. Expanding on ideas of Guillop\'{e} and others, we use high-energy corrections to find representatives of the $K$-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.
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