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One-dimensional Schrödinger operators with general point interactions


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.

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TitleOne-dimensional Schrödinger operators with general point interactions
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 4-15
MathSciNet MR3088074
zbMATH 1289.47089
MilestonesReceived 15/09/2012
CopyrightThe 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 

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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.


@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 = {},

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