论文标题
在$ s $ -matrix上，schrödinger运营商与非本地$δ$ - 互动
On the $S$-matrix of Schrödinger operator with nonlocal $δ$-interaction
论文作者
论文摘要
使用Lax-Phillips散射理论方法研究了具有非本地$δ$ - 互动的Schrödinger操作员。建立了LAX-Phillips方法的适用条件，以非循环功能为角度。获得了$ S $ -MATRIX的两个公式。第一个涉及Krein-Naimark分解公式和Weyl-Titchmarsh功能，而第二个函数基于修改后的反射和传输系数。 $ s $ -matrix $ s（z）$在下半平面$ \ mathbb {c _-} $中是分析的。否则，$ s（z）$是$ \ mathbb {c _-} $中的meromorphic矩阵值函数，其属性与相应的schrödinger操作员的属性密切相关。给出了$ s $ - 标准的示例。
Schrödinger 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 Schrödinger 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 Schrödinger operator. Examples of $S$-matrices are given.
