Absolute Continuity of Hamiltonians with von Neumann Wigner Potentials

DOI10.2307/2048326zbMath0726.34072OpenAlexW4239404582MaRDI QIDQ3348357

Horst Behncke

Publication date: 1991

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

Full work available at URL: https://doi.org/10.2307/2048326

zbMATH Keywords

spectrumlimiting absorption principleDirac systemsabsolute continuitySturm-Liouville differential operatorfinite resonance setsubordinary

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (15)

The spectral function for Sturm-Liouville problems where the potential is of Wigner-von Neumann type or slowly decaying ⋮ Zeroes of the spectral density of the Schrödinger operator with the slowly decaying Wigner-von Neumann potential ⋮ Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials ⋮ Zeroes of the spectral density of discrete Schrödinger operator with Wigner-von Neumann potential ⋮ Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a. e. convergence of integral operators ⋮ Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach ⋮ On eigenvalues of the one-dimensional Dirac operator with oscillatory decreasing potential ⋮ Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials ⋮ On the application of some of M. G. Krein's results to the spectral analysis of Sturm-Liouville operators ⋮ Resonances and viscosity limit for the Wigner-von Neumann-type Hamiltonian ⋮ Spectral analysis of fourth order differential operators III ⋮ Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results ⋮ Absolute continuity and spectral concentration for slowly decaying potentials ⋮ Absolutely continuous spectra for matrix Dirac systems ⋮ Absolute continuity of Hamiltonians with von Neumann Wigner potentials. II

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