Coupling constant thresholds of perturbed periodic Hamiltonians

DOI10.1063/1.532516zbMath0935.81019OpenAlexW2042661950MaRDI QIDQ4701654

Silvestro Fassari, Martin Klaus

Publication date: 21 November 1999

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

Full work available at URL: http://hdl.handle.net/10919/47036

zbMATH Keywords

asymptotic behaviorcontinuous spectrumeigenvaluesSchrödinger operatorscoupling constant threshold

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Perturbation theory of linear operators (47A55) General theory of ordinary differential operators (47E05) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (9)

Stability of standing waves for NLS with perturbed Lamé potential ⋮ A note on the asymptotic and threshold behaviour of discrete eigenvalues inside the spectral gaps of the difference operator with a periodic potential ⋮ Asymptotic stability of the vacuum solution for one‐dimensional nonlinear Klein‐Gordon equations with a perturbed one‐gap periodic potential with and without an eigenvalue ⋮ Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions ⋮ Asymptotic behaviors of the eigenvalues of Schrödinger operator with critical potential ⋮ On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D ⋮ Convergent expansions of eigenvalues of the generalized Friedrichs model with a rank-one perturbation ⋮ Perturbations of eigenvalues embedded at threshold: Two-dimensional solvable models ⋮ On perturbation of eigenvalues embedded at thresholds in a two channel model

Cites Work

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• On the bound state of Schrödinger operators in one dimension
• Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• On the absorption of eigenvalues by continuous spectrum in regular perturbation problems
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• Inverse scattering by a local impurity in a periodic potential in one dimension
• Exact behavior of Jost functions at low energy
• Spectral properties of the Kronig–Penney Hamiltonian with a localized impurity
• Continuity of the S matrix for the perturbed Hill’s equation

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