Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $S$-matrix of Schr\"odinger operator with nonlocal
  $\delta$-interaction   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.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph