On the S-matrix of Schrodinger operator with nonlocal 6-interaction

• Autorzy: Główczyk Anna , Kużel Sergiusz

Identyfikatory

DOI

10.7494/OpMath.2021.41.3.413

• Języki publikacji: EN

Abstrakty

EN

Schrodinger operators with nonlocal δ-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the S-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The S-matrix S(z) is analytical in the lower half-plane C- when the Schrodinger operator with nonlocal δ-interaction is positive self-adjoint. Otherwise, S(z) is a meromorphic matrix-valued function in C- and its properties are closely related to the properties of the corresponding Schrodinger operator. Examples of S-matrices are given.

Słowa kluczowe

EN

Lax-Phillips scattering scheme; scattering matrix; S-matrix; nonlocal -interaction; non-cyclic function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 3
• Strony: 413--435
• Opis fizyczny: BIbliogr, 20 poz.

Twórcy

autor

Główczyk Anna

• AGH University of Science and Technology Faculty of Applied Mathematics AGH al. Mickiewicza 30, 30-059 Kraków

• https://orcid.org/0000-0001-5205-827X

autor

Kużel Sergiusz

• AGH University of Science and Technology Faculty of Applied Mathematics AGH al. Mickiewicza 30, 30-059 Kraków

• https://orcid.org/0000-0002-4322-6611

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).