A unified approach to eigenvalues and resonances of Schrödinger operators using Fredholm determinants

DOI10.1016/0022-247X(87)90303-9zbMath0622.35049OpenAlexW2093663771MaRDI QIDQ1090851

Helge Holden, Friedrich Gesztesy

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-247x(87)90303-9

zbMATH Keywords

continuous spectrumeigenvaluesSchrödinger operatorFredholm determinantsresonancesanalytic structurethreshold behaviour

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10)

Related Items

On absence of threshold resonances for Schrödinger and Dirac operators, The Fermi golden rule and its form at thresholds in odd dimensions, Linear and orbital stability analysis for solitary-wave solutions of variable-coefficient scalar-field equations, On perturbation of thresholds in essential spectrum under coexistence of virtual level and spectral singularity, Spectra of operator pencils with small 𝒫𝒯-symmetric periodic perturbation, On the bifurcation of thresholds of the essential spectrum with a spectral singularity, Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics, Perturbations of the continuous spectrum of a certain nonlinear two-dimensional operator sheaf, Evans functions, Jost functions, and Fredholm determinants, Counting Function of Characteristic Values and Magnetic Resonances, Threshold properties of matrix-valued Schrödinger operators. II: Resonances, Perturbations of eigenvalues embedded at threshold: Two-dimensional solvable models, On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions, On perturbation of eigenvalues embedded at thresholds in a two channel model, The generalized Birman–Schwinger principle, Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation of resonances in quantum mechanics
• Perturbation theory for eigenvalues and resonances of Schrödinger hamiltonians
• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
• Perturbation of resonances
• Notes on infinite determinants of Hilbert space operators
• On the absorption of eigenvalues by continuous spectrum in regular perturbation problems