# Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

@article{Kovark2011EigenvalueBF, title={Eigenvalue bounds for two-dimensional magnetic Schr{\"o}dinger operators}, author={Hynek Kovar{\'i}k}, journal={arXiv: Spectral Theory}, year={2011}, volume={1}, pages={363-387} }

We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We also show how the corresponding upper bounds depend on the properties of the magnetic field and discuss their connection with Hardy-type inequalities.

## 11 Citations

Eigenvalue Bound for Schrödinger Operators with Unbounded Magnetic Field

- MathematicsReports on Mathematical Physics
- 2020

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…

A magnetic contribution to the Hardy inequality

- Mathematics
- 2014

We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not…

On the improvement of the Hardy inequality due to singular magnetic fields

- Mathematics, PhysicsCommunications in Partial Differential Equations
- 2020

Abstract We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and…

Eigenvalue bounds for radial magnetic bottles on the disk

- MathematicsAsymptot. Anal.
- 2012

An upper bound on the number of eigenvalues of H smaller than any positive value is obtained, which involves the minimum of B and the square of the L^2 -norm of A( r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centerde in the origin.

Estimates for the number of eigenvalues of two dimensional Schrödinger operators lying below the essential spectrum

- Mathematics
- 2016

The celebrated Cwikel-Lieb_Rozenblum inequality gives an upper estimate for the number of negative eigenvalues of Schroedinger operators in dimension three and higher. The situation is much more…

The Hardy inequality and the heat equation with magnetic field in any dimension

- Mathematics
- 2014

ABSTRACT In the Euclidean space of any dimension d, we consider the heat semigroup generated by the magnetic Schrödinger operator from which an inverse-square potential is subtracted to make the…

Resolvent Expansion and Time Decay of the Wave Functions for Two-Dimensional Magnetic Schrödinger Operators

- Mathematics
- 2014

We consider two-dimensional Schrödinger operators H(B, V) given by Eq. (1.1) below. We prove that, under certain regularity and decay assumptions on B and V, the character of the expansion for the…

Duality Method in the Exact Controllability of Hyperbolic Electromagnetic Equations

- Mathematics
- 2015

In this paper, we address the exact controllability problem for the hyperbolic electromagnetic equation, which plays an important role in the research of quantum mechanics. Typical techniques such as…

First observation of the Top Quark at the Large Hadron Collider

- Physics
- 2011

This thesis presents the measurement of the top quark pair production cross section in the CMS detector at the CERN Large Hadron Collider (LHC). At LHC, the top quark is produced predominantly…

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