Schrödinger operators with many bound states

DOI10.1215/S0012-7094-07-13612-3zbMath1114.34065arXivmath-ph/0412091OpenAlexW1985489837MaRDI QIDQ860117

David Damanik, Remling, Christian

Publication date: 23 January 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0412091

zbMATH Keywords

spectral propertiessingular Sturm-Liouville operatorinfluence of the structure of the discrete spectrum on the potentialinverse Lieb-Thirring inequalities

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) General theory of ordinary differential operators (47E05) Inverse problems involving ordinary differential equations (34A55) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (11)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ A relation between the positive and negative spectra of elliptic operators ⋮ The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum ⋮ Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law ⋮ Discrete and embedded eigenvalues for one-dimensional Schrödinger operators ⋮ Absolutely continuous spectrum of a Dirac operator in the case of a positive mass ⋮ Multi-dimensional Schrödinger operators with some negative spectrum ⋮ Relations between two parts of the spectrum of a Schrödinger operator and other remarks on the absolute continuity of the spectrum in a typical case ⋮ Bound states of discrete Schrödinger operators with super-critical inverse square potentials ⋮ Schrödinger operators with few bound states ⋮ Discrete spectrum for Schrödinger operators with oscillating decaying potentials

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