Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

DOI10.1016/j.jfa.2003.07.015zbMath1061.47041arXivmath-ph/0308012OpenAlexW2025767094MaRDI QIDQ1888355

Boris Vainberg, Stanislav Alekseevich Molchanov

Publication date: 23 November 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0308012

zbMATH Keywords

Schrödinger operatorabsolutely continuous spectrum\(L^2\)-conjecture

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)

Related Items (5)

On the preservation of absolutely continuous spectrum for Schrödinger operators ⋮ On the AC spectrum of one-dimensional random Schrödinger operators with matrix-valued potentials ⋮ Unnamed Item ⋮ Boris Rufimovich Vainberg ⋮ Integral problem for Schrödinger-type equations with the general elliptic part

Cites Work

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• One-dimensional Schrödinger operators with random decaying potentials
• Stochastic Schrödinger operators and Jacobi matrices on the strip
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• Discrete and continuous boundary problems
• First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator

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