• Corpus ID: 235446786

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

@inproceedings{Sorowen2021EstimationOT,
title={Estimation of the number of negative eigenvalues of magnetic Schr\"odinger operators in a strip},
author={Ben Sorowen},
year={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 that the estimate does not hold in absence of Aharonov-Bohm magnetic field.

## References

SHOWING 1-10 OF 70 REFERENCES
Spectral estimates for magnetic operators
• Mathematics
• 1996
The well-known CLR-estimate for the number of negative eigenvalues of the Schrodinger operator $-\Delta+V$ is generalized to a class of second order magnetic operators, generalizing the magnetic
Eigenvalue bounds for two-dimensional magnetic Schrödinger operators
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
Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip
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 the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator
• Mathematics
• 1998
To Mikhail Shl emovich Birman on the occasion of his 70-th birthday, as a sign of friendship and admiration Introduction. Eigenvalue estimates for operators of mathematical physics play
Negative Eigenvalues of Two-Dimensional Schrödinger Operators
• Mathematics
• 2011
We prove a certain upper bound for the number of negative eigenvalues of the Schrödinger operator H = −Δ − V in $${\mathbb{R}^{2}.}$$R2.
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,
A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
• Mathematics
• 1998
We give a proof of the Lieb-Thirring inequality in the critical case d=1, γ = 1/2, which yields the best possible constant.