One-dimensional Schrödinger operators with general point interactions

Abstract

We consider various forms of boundary-value conditions for general one-dimensional Schrödinger operators with point interactions that include $\delta$- and $\delta'$- interactions, $\delta'$- potential, and $\delta$- magnetic potential. We give most simple spectral properties of such operators, and consider a possibility of finding their norm resolvent approximations.

Key words: 1D Schrödinger operator, point interaction, negative eigenvalues, resolvent approximation.

Full Text

Article Information

Title	One-dimensional Schrödinger operators with general point interactions
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 4-15
MathSciNet	MR3088074
zbMATH	1289.47089
Milestones	Received 15/09/2012
Copyright	The Author(s) 2013 (CC BY-SA)

Authors Information

J. F. Brasche
Institute of Mathematics, TU Clausthal, Clausthal, Germany

L. P. Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 

Citation Example

J. F. Brasche and L. P. Nizhnik, One-dimensional Schrödinger operators with general point interactions, Methods Funct. Anal. Topology 19 (2013), no. 1, 4-15.

BibTex

@article {MFAT675,
    AUTHOR = {Brasche, J. F. and Nizhnik, L. P.},
     TITLE = {One-dimensional   Schrödinger operators  with general point interactions},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {4-15},
      ISSN = {1029-3531},
  MRNUMBER = {MR3088074},
 ZBLNUMBER = {1289.47089},
       URL = {http://mfat.imath.kiev.ua/article/?id=675},
}