- Tytuł:
- On the $S$-matrix of Schrödinger operator with nonlocal $\delta$-interaction
- Autorzy:
-
Główczyk, Anna
Kużel, Sergiusz - Powiązania:
- https://bibliotekanauki.pl/articles/2051910.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Lax-Phillips scattering scheme
scattering matrix
S-matrix
nonlocal -interaction
non-cyclic function - Opis:
- 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 $\mathbb{C}$_ when the Schrodinger operator with nonlocal δ-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 Schrodinger operator. Examples of S-matrices are given.
- Źródło:
-
Opuscula Mathematica; 2021, 41, 3; 413-435
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł