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# Multi-dimensional Schrödinger operators with point interactions

### Abstract

We study two- and three-dimensional matrix Schrödinger operators with $m\in \Bbb N$ point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by the other authors in this field. For instance, we parametrize all self-adjoint extensions of the initial minimal symmetric Schrödinger operator by abstract boundary conditions and characterize their spectra. Particularly, we find a sufficient condition in terms of distances and intensities for the self-adjoint extension $H_{\alpha,X}^{(3)}$ to have $m'$ negative eigenvalues, i.e., $\kappa_-(H_{\alpha,X}^{(3)})=m'\le m$. We also give an explicit description of self-adjoint nonnegative extensions.

### Article Information

 Title Multi-dimensional Schrödinger operators with point interactions Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 2, 126-143 MathSciNet MR2849473 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Nataly Goloshchapova
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 74 R. Luxemburg, Donetsk, 83114, Ukraine

### Citation Example

Nataly Goloshchapova, Multi-dimensional Schrödinger operators with point interactions, Methods Funct. Anal. Topology 17 (2011), no. 2, 126-143.

### BibTex

@article {MFAT541,
AUTHOR = {Goloshchapova, Nataly},
TITLE = {Multi-dimensional Schrödinger operators with  point interactions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {2},
PAGES = {126-143},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=541},
}