Year: 2019
Type: preprint
Abstract: We review some results on the spectral theory of Schr{ö}dinger and Dirac operators. We focus on two aspects: the existence of embbedded eigen-values in the essential spectrum and the limiting absorption principle. They both are important for Physics, in general, and for Scattering theory, in particular. We chose to include a special form of oscillations in the potential of the considered operators to illustrate the diversity of behaviours that can exist in the two selected topics. Concerning the limiting absorption principle, we discuss several methods to prove it. To known, old or recent results, we added some unpublished results from Mbarek's Phd Thesis.
Source: arXiv (Cornell University)
Author: Jecko, Thierry
Institution: Analyse, Géométrie et Modélisation
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2945795985