Counting Schrödinger Boundstates: Semiclassics and Beyond

DOI10.1007/978-0-387-85650-6_14zbMath1172.35046arXiv0803.3138OpenAlexW1598765163MaRDI QIDQ3627662

Grigori Rozenblum, Michael Solomyak

Publication date: 13 May 2009

Published in: Sobolev Spaces in Mathematics II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.3138

zbMATH Keywords

Weyl asymptoticRozenblum-Lieb-Cwikel inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10)

Related Items

A simple criterion for the existence of nonreal eigenvalues for a class of 2D and 3D Pauli operators, On spectral estimates for the Schrödinger operators in global dimension 2, On spectral estimates for Schrödinger-type operators: the case of small local dimension, On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\), Seven useful questions in density functional theory, Number of eigenvalues for dissipative Schrödinger operators under perturbation, Sharp two-sided heat kernel estimates of twisted tubes and applications, The lowest eigenvalue of Schrödinger operators on compact manifolds, Bargmann type estimates of the counting function for general Schrödinger operators, Lieb-Thirring type inequalities for non-self-adjoint perturbations of magnetic Schrödinger operators, On the negative spectrum of the hierarchical Schrödinger operator, On the mathematical work of Mikhail Zakharovich Solomyak, Spectral estimates for Schrödinger operators with sparse potentials on graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalue estimates for Schrödinger operators on metric trees
• On the Schrödinger equation and the eigenvalue problem
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator
• The Rozenblum-Lieb-Cwikel inequality for Markov generators
• Regular and pathological eigenvalue behavior for the equation \(-\lambda u=Vu\) on the semiaxis
• The uncertainty principle
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• [https://portal.mardi4nfdi.de/wiki/Publication:4893803 The negative discrete spectrum of a two-dimensional Schr�dinger operator]
• The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius
• On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential.