Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice

Fumio Hiroshima; Zahriddin Muminov; Utkir Kuljanov

Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice

Spectral Theory 2018-04-17 v1

Authors: Fumio Hiroshima , Zahriddin Muminov , Utkir Kuljanov

Abstract

Eigenvalue behaviors of Schr\"odinger operator defined on $n$ -dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$ , and lower super-threshold resonance appeared for $n=1$ .

Keywords

discrete Schrödinger operator delta potential n-dimensional lattice threshold eigenvalue threshold resonance

Cite

@article{arxiv.1804.05339,
  title  = {Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice},
  author = {Fumio Hiroshima and Zahriddin Muminov and Utkir Kuljanov},
  journal= {arXiv preprint arXiv:1804.05339},
  year   = {2018}
}

Comments

30 pages, 6 figures, 4 tables

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