# A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator

@article{Hundertmark1998ASB, title={A sharp bound for an eigenvalue moment of the one-dimensional Schr{\"o}dinger operator}, author={Dirk Hundertmark and Elliott H. Lieb and Lawrence E. Thomas}, journal={Advances in Theoretical and Mathematical Physics}, year={1998}, volume={2}, pages={329-341} }

We give a proof of the Lieb-Thirring inequality in the critical case d=1, γ = 1/2, which yields the best possible constant.

## 12 Citations

New bounds on the Lieb-Thirring constants

- Mathematics
- 2000

Abstract.Improved estimates on the constants Lγ,d, for 1/2<γ<3/2, d∈N, in the inequalities for the eigenvalue moments of Schrödinger operators are established.

Critical Lieb-Thirring bounds for one-dimensional Schrodinger operators and Jacobi matrices with regular ground states

- Mathematics
- 2007

This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998

Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators

- Mathematics
- 2007

This thesis is devoted to quantitative questions about the discrete spectrum of Schrodinger-type operators.
In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬value…

A Sharp Lieb-Thirring Inequality for Functional Difference Operators

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2021

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of…

Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law

- Mathematics
- 2010

We consider the Schrödinger operator H = −Δ − V(x), V > 0, acting in the space $ L^2 (\mathbb{R}^d) $ and study relations between the behavior of V at infinity and properties of the negative spectrum…

A simple proof of a theorem of Laptev and Weidl

- Mathematics
- 1999

A new and elementary proof of a recent result of Laptev and Weidl is given. It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger operators with matrix valued potentials.

Negative spectra of elliptic operators

- Mathematics
- 2012

We establish different estimates for the sums of negative eigenvalues of elliptic operators. Our proofs are based on a property of the eigenvalue sums that might be viewed as a certain convexity with…

Equivalence of Sobolev inequalities and Lieb-Thirring inequalities

- Mathematics
- 2010

We show that, under very general definitions of a kinetic energy operator T, the Lieb–Thirring inequalities for sums of eigenvalues of T - V can be derived from the Sobolev inequality appropriate to…

A trace formula and Schmincke inequality on the half-line

- Mathematics
- 2008

In this paper we derive a trace formula for the Schrodinger operator on the half-line. As a consequence we obtain a Schmincke type inequality with sharp constant. The main tool in our investigation…