Spectral and threshold analysis of a small rank perturbation of the discrete Laplacian

DOI10.1016/j.jmaa.2020.124827zbMath1473.81071OpenAlexW3111408347MaRDI QIDQ1997228

Zahriddin I. Muminov, Shukhrat Lakaev, Shukhrat Alladustov

Publication date: 1 March 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2020.124827

zbMATH Keywords

latticeeigenvaluesdiscrete Schrödinger operatorsthreshold resonance

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Discrete version of topics in analysis (39A12) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Discrete operational calculus (44A55)

Related Items (14)

On the number of eigenvalues of the lattice model operator in one-dimensional case ⋮ Invariant subspaces of the Schrödinger operator with a finite support potential ⋮ On the spectrum of two-particle Schrödinger operator with point interaction ⋮ The spectrum of a non-local discrete Schrödinger operator with a delta potential on the one-dimentional lattice ⋮ Infiniteness of the discrete spectrum of two-particle discrete Schrödinger operators ⋮ On the number and locations of eigenvalues of the discrete Schrödinger operator on a lattice ⋮ The essential spectrum of a three particle Schrödinger operator on lattices ⋮ On the discrete spectrum of a one-dimensional discrete Schrödinger operator with a perturbation of rank one ⋮ On the existence of bound states of a system of two fermions on the two-dimensional cubic lattice ⋮ Puiseux series expansion for eigenvalue of the generalized Friedrichs model with the perturbation of rank one ⋮ The existence and asymptotics of eigenvalues of Schrödinger operator on two dimensional lattices ⋮ On the number and location of eigenvalues of the two particle Schrödinger operator on a lattice ⋮ On the essential spectrum of three-particle discrete Schrödinger operators with short-range potentials ⋮ Threshold analysis of the one-rank perturbation non-local discrete Laplacian

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