The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential

DOI10.1007/s11232-006-0056-yzbMath1177.34107arXivmath-ph/0508013OpenAlexW3105394806MaRDI QIDQ1047976

Denis I. Borisov, Rustem R. Gadyl'shin

Publication date: 9 January 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0508013

zbMATH Keywords

asymptotic behaviorperturbationSchrödinger operatorspectrum

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (7)

Resonances for random highly oscillatory potentials ⋮ Oscillatory and Localized Perturbations of Periodic Structures and the Bifurcation of Defect Modes ⋮ Bound States for Rapidly Oscillatory Schrödinger Operators in Dimension 2 ⋮ Some singular perturbations of periodic operators ⋮ Scattering and Localization Properties of Highly Oscillatory Potentials ⋮ Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients ⋮ Defect modes for dislocated periodic media

Cites Work

• Unnamed Item
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Asymptotic approximation for a new eigenvalue in linear problems without a threshold
• Local perturbations of the Schrödinger operator on the axis

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