Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states

DOI10.1007/s00220-008-0453-1zbMath1158.35021arXiv0707.0998OpenAlexW3105772522MaRDI QIDQ956640

Barry Simon, Rupert L. Frank, Timo Weidl

Publication date: 25 November 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.0998

zbMATH Keywords

Schrödinger operatorsperturbationsJacobi matricescomparison theoremsLieb-Thirring bounds

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Applications of operator theory in the physical sciences (47N50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (20)

Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Lieb-Thirring inequalities for complex finite gap Jacobi matrices ⋮ Optimal Hardy inequalities for Schrödinger operators on graphs ⋮ Lieb—Thirring type bounds for perturbed Schrödinger operators with single-well potentials ⋮ Optimal Hardy inequality for fractional Laplacians on the integers ⋮ Optimal Hardy weights on the Euclidean lattice ⋮ A non-local quasi-linear ground state representation and criticality theory ⋮ Finite gap Jacobi matrices. III: Beyond the Szegő class ⋮ Eigenvalue estimates for Schrödinger operators on metric trees ⋮ Finite gap Jacobi matrices. I: The isospectral torus ⋮ Finite gap Jacobi matrices. II: The Szegő class ⋮ Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices ⋮ Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory ⋮ Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices ⋮ Generalized Solutions and Spectrum for Dirichlet Forms on Graphs ⋮ A probabilistic approach to the Liouville property for Schrödinger operators with an application to infinite configurations of balls ⋮ Nonlinear ground state representations and sharp Hardy inequalities ⋮ Remarks on periodic Jacobi matrices on trees ⋮ Finite gap Jacobi matrices: An announcement ⋮ On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Lieb-Thirring inequalities for Schrödinger operators with virtual level
• Spectral estimates for two-dimensional Schrödinger operators with application to quantum layers
• Perturbations of orthogonal polynomials with periodic recursion coefficients
• Comparison theorems for the gap of Schrödinger operators
• Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
• Lieb-Thirring inequalities for Jacobi matrices
• Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices
• Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
• Schrödinger semigroups
• On Schrödinger's factorization method for Sturm-Liouville operators

This page was built for publication: Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states