# Negative Eigenvalues of Two-Dimensional Schrödinger Operators

@article{Grigoryan2011NegativeEO, title={Negative Eigenvalues of Two-Dimensional Schr{\"o}dinger Operators}, author={Alexander Grigor’yan and Nikolai S. Nadirashvili}, journal={Archive for Rational Mechanics and Analysis}, year={2011}, volume={217}, pages={975-1028} }

We prove a certain upper bound for the number of negative eigenvalues of the Schrödinger operator H = −Δ − V in $${\mathbb{R}^{2}.}$$R2.

## 21 Citations

On negative eigenvalues of two‐dimensional Schrödinger operators

- Mathematics
- 2014

The paper presents estimates for the number of negative eigenvalues of a two‐dimensional Schrödinger operator in terms of L log L‐type Orlicz norms of the potential and proves a conjecture by N.N.…

A lower bound for the number of negative eigenvalues of Schr\"{o}dinger operators

- Mathematics
- 2014

We prove a lower bound for the number of negative eigenvalues for a Schr\"{o}dinger operator on a Riemannian manifold via the integral of the potential.

Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains

- MathematicsSt. Petersburg Mathematical Journal
- 2019

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\"odinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm…

On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials

- Mathematics
- 2019

We present upper estimates for the number of negative eigenvalues of two-dimensional Schroedinger operators with potentials generated by Ahlfors regular measures of arbitrary dimension $\alpha\in (0,…

Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip

- MathematicsJournal of Mathematics
- 2018

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve…

On spectral estimates for the Schrödinger operators in global dimension 2

- Mathematics
- 2012

The problem of finding eigenvalue estimates for the Schrodinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently. In the…

Estimation of the number of negative eigenvalues of magnetic Schr\"odinger operators in a strip

- Physics
- 2021

An upper estimate for the number of negative eigenvalues below the essential spectrum for the magnetic Schrödinger operator with Aharonov-Bohm magnetic field in a strip is obtained. Its further shown…

On the discrete spectrum of Schrödinger operators with Ahlfors regular potentials in a strip

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

Conformal volume and eigenvalue problems

- Mathematics
- 2017

We prove inequalities for Laplace eigenvalues on Riemannian manifolds generalising to higher eigenvalues two classical inequalities for the first Laplace eigenvalue - the inequality in terms of the…

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For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V,\ V\ge 0,$ we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues (bound states), as the…

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