BooksStandalone TitlesCollected Volumepp. 253–275

The state of the Lieb–Thirring conjecture

  • Lukas Schimmer

    Royal Swedish Academy of Sciences, Djursholm, Sweden
The state of the Lieb–Thirring conjecture cover
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Abstract

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.