The state of the Lieb–Thirring conjecture
In 1976 Lieb and Thirring established upper bounds on sums of powers of the negative eigenvalues of a Schrödinger operator in terms of semiclassical phase-space integrals. Over the last 45 years the optimal constants in these inequalities, the values of which were conjectured by Lieb and Thirring, have been subject of intense investigations. We aim to review existing results.
Spectral properties of discrete and continuous Schrödinger operators
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- Mathematical Sciences
Published inThe Physics and Mathematics of Elliott Lieb: Volume II
Pages253 - 275
- AM (Accepted Manuscript)
Rights holder© EMS Press
Publisher statementThis book chapter was accepted for publication in the book The Physics and Mathematics of Elliott Lieb: Volume II [© EMS Press]. The definitive published version is available at https://doi.org/10.4171/90-2/39