2024-03-28T11:12:52Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00025092
2023-01-16T04:15:50Z
697:698:699
Does Levinson’s theorem count complex eigenvalues?
Nicoleau, F.
74835
Parra, D.
74836
Richard, Serge
74837
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.
journal article
AIP Publishing
2017-10
application/pdf
Journal of Mathematical Physics
58
102101
102101
https://doi.org/10.1063/1.5004574
http://hdl.handle.net/2237/27311
0022-2488
https://nagoya.repo.nii.ac.jp/record/25092/files/1_5004574.pdf
eng
https://doi.org/10.1063/1.5004574
Copyright 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).