The existence and location of eigenvalues of the one particle discrete Schroedinger operators

14 May 2015 Lakaev Saidakhmat N. Ozdemir Ender

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum such that one of them is situated below the bottom of the essential spectrum, and other one above its top...

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Categories


  • SPECTRAL THEORY
  • MATHEMATICAL PHYSICS
  • MATHEMATICAL PHYSICS