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Browsing by Subject "S-matrix"

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  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Badanie operatora Schrödingera z PT-symetrycznym potencjałem
    (Data obrony: 2014-07-10) Zakrzewski, Bartosz
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Badanie operatorów $0$-zaburzonych za pomocą schematu Laxa-Phillipsa w teorii rozproszenia
    (Data obrony: 2014-03-14) Rzepka, Barbara
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the S-matrix of Schrödinger operator with nonlocal δ-interaction
    (Wydawnictwa AGH, 2021) Główczyk, Anna; Kużel, Sergiusz
    Schrödinger operators with nonlocal $\delta$-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 $\mathbb{C}_{−}$ when the Schrödinger operator with nonlocal $\delta$-interaction is positive self-adjoint. Otherwise, $S(z)$ is a meromorphic matrix-valued function in $\mathbb{C}_{−}$ and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of $S$-matrices are given.
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Własności współczynników odbicia i transmisji w teorii rozproszenia
    (Data obrony: 2016-02-22) Jeżów, Katarzyna
    Wydział Matematyki Stosowanej