2021-09-21T02:42:52Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000250922021-03-01T13:45:49ZDoes Levinson’s theorem count complex eigenvalues?Nicoleau, F.Parra, D.Richard, SergeCopyright 2017 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.The following article appeared in (Journal of Mathematical Physics. v.58, 2017, p.102101) and may be found at (https://doi.org/10.1063/1.5004574).By considering a quantum-mechanical system with complex eigenvalues, we show that indeed Levinson’s theorem extends to the non self-adjoint setting. The perturbed system corresponds to a realization of the Schrödinger operator with inverse square potential on the half-line, while the Dirichlet Laplacian on the half-line is chosen for the reference system. The resulting relation is an equality between the number of eigenvalues of the perturbed system and the winding number of the scattering system together with additional operators living at 0-energy and at infinite energy.AIP Publishing2017-10engjournal articlehttp://hdl.handle.net/2237/27311https://nagoya.repo.nii.ac.jp/records/250920022-2488Journal of Mathematical Physics58102101102101https://nagoya.repo.nii.ac.jp/record/25092/files/1_5004574.pdfapplication/pdf387.4 kB2018-10-01