Schrödinger operators with nonlocal potentials

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.

Full Text

Article Information

Title	Schrödinger operators with nonlocal potentials
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 3, 199-210
MathSciNet	MR3136727
zbMATH	1289.34237
Milestones	Received 24/12/2012; Revised 25/06/2013
Copyright	The 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},
}