International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Semiclassical Resonances via Meromorphy of the Resolvent and the S-Matrix

  • Soumia Belmouhoub1*
  • Bekkai Messirdi2
  • Abderrahmane Senoussaoui3
  1. Department of Mathematics and Informatics, University of Mostaganem
  2. Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO). University of Oran1, Ahmed Benbella, Oran, Algeria.
  3. Department of Mathematics, Faculy of Exact and Applicable Sciences. University of Oran1 Ahmed Ben Bella, Algeria., Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO), Algeria.

* Corresponding author

Abstract

The purpose of this paper is to describe the basic problems of resonances via meromorphic continuation of the resolvent and the scattering matrix. An example from mathematical physics is given by investigating the poles of the resolvent of semiclassical Schr ¨odinger operators and Born-Oppenheimer Hamiltonians. Mathematical techniques, dilation-analyticity and Feshbach reduction are used here for the characterization of resonances of these Hamiltonians.

How to Cite

S. Belmouhoub, B. Messirdi, A. Senoussaoui, Semiclassical Resonances via Meromorphy of the Resolvent and the S-Matrix, Int. J. Anal. Appl. 18 (2020), 262–276. https://doi.org/10.28924/2291-8639-18-2020-262

BibTeX
@article{Belmouhoub2020,
  author  = {Belmouhoub, Soumia and Messirdi, Bekkai and Senoussaoui, Abderrahmane},
  title   = {Semiclassical Resonances via Meromorphy of the Resolvent and the S-Matrix},
  journal = {Int. J. Anal. Appl.},
  volume  = {18},
  year    = {2020},
  pages   = {262--276},
  doi     = {10.28924/2291-8639-18-2020-262}
}

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