On the number of bound states for Schrödinger operators with operator-valued potentials

DOI10.1007/BF02384503zbMath1030.35129MaRDI QIDQ1416629

Dirk Hundertmark

Publication date: 15 December 2003

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

singular valuesweak type estimatesLieb-Thirring inequalityCLR estimate

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Operator ideals (47L20)

Related Items (14)

Lieb-Thirring inequalities for generalized magnetic fields ⋮ Cwikel's bound reloaded ⋮ Quantitative bounds versus existence of weakly coupled bound states for Schrödinger type operators ⋮ Estimates for negative eigenvalues of a random Schrödinger operator ⋮ Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law ⋮ Cwikel's theorem and the CLR inequality ⋮ Advances in Dixmier traces and applications ⋮ Number of bound states of Schrödinger operators with matrix-valued potentials ⋮ Lieb-Thirring inequalities for geometrically induced bound states ⋮ Weighted supermembrane toy model ⋮ On some new spectral estimates for Schrödinger-like operators ⋮ The Lieb-Thirring inequality revisited ⋮ Counting bound states with maximal Fourier multipliers ⋮ On Riesz Means of Eigenvalues

Cites Work

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• On the Schrödinger equation and the eigenvalue problem
• A new proof of the Cwikel-Lieb-Rosenbljum bound
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
• Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
• New bounds on the Lieb-Thirring constants
• A simple proof of a theorem of Laptev and Weidl
• Sharp Lieb-Thirring inequalities in high dimensions.
• On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)
• Thomas-fermi and related theories of atoms and molecules
• Bounds on the eigenvalues of the Laplace and Schroedinger operators

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