- PII
- 10.31857/S0374064123020127-1
- DOI
- 10.31857/S0374064123020127
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 59 / Issue number 2
- Pages
- 270-274
- Abstract
- We consider the Schrödinger operator on the plane with bounded potential, where is a real potential, and are compactly supported complex potentials, and is a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrödinger operator consists of a pair of isolated eigenvalues and the essential spectrum of the operator has a virtual level at its lower edge and a spectral singularity inside. Additionally, we assume that there is a certain superposition of eigenvalues of the operator with the virtual level and spectral singularity of the operator; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.
- Keywords
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 9
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