Bound states of discrete Schrödinger operators with super-critical inverse square potentials

DOI10.1090/S0002-9939-06-08550-9zbMath1110.47019arXivmath/0509110OpenAlexW2163854232WikidataQ57343922 ScholiaQ57343922MaRDI QIDQ3420092

Gerald Teschl, David Damanik

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509110

zbMATH Keywords

oscillation theorydiscrete Schrödinger operatorsbound states

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear difference operators (47B39) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (7)

An application of Phragmén-Lindelöf theorem to the existence of ground state solutions for the generalized Schrödinger equation with optimal control ⋮ Expansion of eigenvalues of the perturbed discrete bilaplacian ⋮ On the spectrum of Schrödinger-type operators on two dimensional lattices ⋮ Bounds on the discrete spectrum of lattice Schrödinger operators ⋮ Bound states of Schrödinger-type operators on one and two dimensional lattices ⋮ Iterative reconstruction algorithms for solving the Schrödinger equations on conical spaces ⋮ Threshold analysis of the one-rank perturbation non-local discrete Laplacian

Cites Work

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• Half-line Schrödinger operators with no bound states
• Schrödinger operators with many bound states
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• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign
• Sum rules for Jacobi matrices and their applications to spectral theory
• Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators.
• Critical coupling constants and eigenvalue asymptotics of perturbed periodic Sturm-Liouville operators
• Oscillation theory and renormalized oscillation theory for Jacobi operators
• Schrödinger operators with few bound states
• On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential Spectrum

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