Eigenvalues of Schrödinger operators with potential asymptotically homogeneous of degree $-2$

DOI10.1090/S0002-9947-08-04479-6zbMath1147.35066arXivmath/0510617OpenAlexW2016431560MaRDI QIDQ3518196

Andrew Hassell, Simon Marshall

Publication date: 7 August 2008

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

Full work available at URL: https://arxiv.org/abs/math/0510617

zbMATH Keywords

eigenvaluesSchrödinger operatorsapproximate eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (6)

On the bound states of Schrödinger operators with δ-interactions on conical surfaces ⋮ Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds ⋮ Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. I. ⋮ Spectral transitions for Aharonov-Bohm Laplacians on conical layers ⋮ Spectral asymptotics of the Dirichlet Laplacian in a conical layer ⋮ Discrete spectrum for Schrödinger operators with oscillating decaying potentials

Cites Work

• Corrections to the classical behavior of the number of bound states of Schrödinger operators
• Pseudo-laplaciens. I
• Scattering theory: some old and new problems
• Spectral asymptotics for manifolds with cylindrical ends
• L²-lower bounds to solutions of one-body Schrödinger equations
• On the asymptotic eigenvalue distribution of a pseudo-differential operator
• The uncertainty principle and sharp gårding inequalities
• Scattering Theory for Automorphic Functions. (AM-87)
• Isoperimetric properties of higher eigenvalues of elliptic operators
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