# The Lieb–Thirring inequality revisited

@article{Frank2018TheLI, title={The Lieb–Thirring inequality revisited}, author={Rupert L. Frank and Dirk Hundertmark and Michal Jex and Phan Th{\`a}nh Nam}, journal={Journal of the European Mathematical Society}, year={2018} }

We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing bounds.

## 18 Citations

Lieb–Thirring constant on the sphere and on the torus

- MathematicsJournal of Functional Analysis
- 2020

Lieb–Thirring inequalities for wave functions vanishing on the diagonal set

- MathematicsAnnales Henri Lebesgue
- 2021

We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave…

The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

- Mathematics
- 2020

We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show…

Lieb-Thirring inequalities and other functional inequalities for orthonormal systems

- Mathematics
- 2021

We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of…

On factorisation of a class of Schrödinger operators

- Mathematics
- 2020

The aim of this paper is to find inequalities for 3/2 moments of the negative eigenvalues of Schrödinger operators on half-line that have a ‘Hardy term’ by using the commutator method.

Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics

- Mathematics
- 2022

We discuss the estimates for the L-norms of systems of functions that are orthonormal in L and H, respectively, and their essential role in deriving good or even optimal bounds for the dimension of…

The Lieb-Thirring inequalities: Recent results and open problems

- Economics
- 2020

This review celebrates the generous gift by Ronald and Maxine Linde for the remodeling of the Caltech mathematics department and the author is very grateful to the editors of this volume for the…

Optimizers for the finite-rank Lieb-Thirring inequality

- Mathematics
- 2021

The finite-rank Lieb-Thirring inequality provides an estimate on a Riesz sum of the N lowest eigenvalues of a Schrödinger operator −∆ − V (x) in terms of an L(R) norm of the potential V . We prove…

The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities

- MathematicsCommunications in Mathematical Physics
- 2021

In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a…

The state of the Lieb--Thirring conjecture

- Physics
- 2022

Estimates on the bound states of a Hamiltonian are of importance in quantum mechanics. For a Schrödinger operator −∆ + V on L(R) with decaying potential V : R → R of particular interest are bounds on…

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