# Spectral estimates for magnetic operators

@article{Melgaard1996SpectralEF, title={Spectral estimates for magnetic operators}, author={Michael Melgaard and G. Rozenblum}, journal={Mathematica Scandinavica}, year={1996}, volume={79}, pages={237-254} }

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 Schrodinger operator. The cofficients in the magnetic operators are variable, they may be nonsmooth, unbounded and some degeneration is allowed.

## 24 Citations

### 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 some new spectral estimates for Schrödinger-like operators

- Mathematics
- 2006

We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with…

### 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 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

### Lieb-Thirring inequality for the Aharonov-Bohm Hamiltonian and eigenvalue estimates

- Physics
- 2002

The diamagnetic inequality is shown for the AharonovBohm Hamiltonian HAB in L(R). As an application the LiebThirring inequality is established for the perturbed Schrodinger operator HAB − V . In…

### On the spectrum of an "even" periodic Schroedinger operator with a rational magnetic flux

- Mathematics, Physics
- 2013

We study the Schr\"odinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the…

### Weighted Spectral Gap and a Unique Continuation Result for the Magnetic Differential Elliptic Operator

- MathematicsJournal of Mathematics Research
- 2022

We prove two different kind of results for the magnetic elliptic operator which are the spectral gap of the magnetic elliptic functional energy and the inverse Poincare inequality which is used to…

### Spectral Properties of Perturbed Multivortex Aharonov-Bohm Hamiltonians

- Mathematics
- 2003

The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm…

### Spectral Shift Function of the Schrödinger Operator in the Large Coupling Constant Limit

- Mathematics
- 2000

The spectral shift function of a Schrödinger operator with a perturbation of definite sign is considered. The asymptotics of the spectral shift function for large coupling constant is studied, and…

### Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring–type estimate

- Mathematics
- 1999

We give the rst Lieb-Thirring type estimate on the sum of the negative eigenvalues of the Pauli operator that behaves as the corresponding semiclassical expression even in the case of strong…