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arXiv · 2609.10478

The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues

Larry Read·Marvin R. Schulz
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Abstract

We prove that the best constant in the one-dimensional Lieb-Thirring inequality with exponent one is $4/(3\sqrt{3}π)$, confirming the Lieb-Thirring conjecture in this case. Moreover, we extend the inequality to operator-valued potentials and obtain the bound $L_{1,d}\leq(2/\sqrt3)L_{1,d}^{\mathrm{cl}}$ in every dimension.

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Larry Read, Marvin R. Schulz. 2026-09-14. The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues. https://arxiv.org/abs/2609.10478

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