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On the $S$-matrix of Schr\"odinger operator with nonlocal $\delta$-interaction by Główczyk, Anna; Kużel, Sergiusz is a scholarly article available to read on EtoBox.

What is On the $S$-matrix of Schr\"odinger operator with nonlocal $\delta$-interaction about?

Schr\"{o}dinger 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 Schr\"{o}dinger 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 Schr\"{o}dinger operator. Examples of $S$-matrices are given.

Author

Główczyk, Anna; Kużel, Sergiusz

Published

2020

Language

EN