Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

Abstract

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.

11 pages

References in corpus (2)

• Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices
• Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers

Cited by in corpus (10)

• Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps
• Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices
• Geometric extensions of many-particle Hardy inequalities
• Eigenvalue estimates for Schroedinger operators on metric trees
• Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices
• Optimal Hardy Inequality for Fractional Laplacians on the Integers
• Finite Gap Jacobi Matrices: An Announcement
• Twelve Tales in Mathematical Physics: An Expanded Heinemann Prize Lecture
• Remarks on Periodic Jacobi Matrices on Trees
• Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices