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Schrödinger operators with nonlocal potentials

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Abstract

We describe selfadjoint nonlocal boundary-value conditions for new exact solvable models of Schrödinger operators with nonlocal potentials. We also solve the direct and the inverse spectral problems on a bounded line segment, as well as the scattering problem on the whole axis for first order operators with a nonlocal potential.

Key words: 1D Schrödinger operator, point interaction, nonlocal potential.


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Article Information

TitleSchrödinger operators with nonlocal potentials
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 3, 199-210
MathSciNet MR3136727
zbMATH 1289.34237
MilestonesReceived 24/12/2012; Revised 25/06/2013
CopyrightThe Author(s) 2013 (CC BY-SA)

Authors Information

Sergio Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Endenicherallee 60, D-53 115 Bonn; HCM, SFB 611, Universitat Bonn; BiBoS (Universities of Bielefeld and Bonn)

Leonid Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine


Citation Example

Sergio Albeverio and Leonid Nizhnik, Schrödinger operators with nonlocal potentials, Methods Funct. Anal. Topology 19 (2013), no. 3, 199-210.


BibTex

@article {MFAT698,
    AUTHOR = {Albeverio, Sergio and Nizhnik, Leonid},
     TITLE = {Schrödinger operators with nonlocal potentials},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {199-210},
      ISSN = {1029-3531},
  MRNUMBER = {MR3136727},
 ZBLNUMBER = {1289.34237},
       URL = {http://mfat.imath.kiev.ua/article/?id=698},
}


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