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The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues
Abstract
We prove that the best constant in the one-dimensional Lieb-Thirring inequality with exponent one is 4/(3√3π), confirming the Lieb-Thirring conjecture in this case. Moreover, we extend the inequality to operator-valued potentials and obtain the bound L1,d≤(2/√3)L1,dcl in every dimension.
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BibTeX
@misc{read2026sharp,
title = {{The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues}},
author = {Larry Read and Marvin R. Schulz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10478},
eprint = {2609.10478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10478},
}
RIS
TY - UNPB
TI - The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues
AU - Larry Read
AU - Marvin R. Schulz
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.10478
UR - https://arxiv.org/abs/2609.10478
AB - We prove that the best constant in the one-dimensional Lieb-Thirring inequality with exponent one is 4/(3√3π), confirming the Lieb-Thirring conjecture in this case. Moreover, we extend the inequality to operator-valued potentials and obtain the bound L_1,d≤(2/√3)L_1,d^cl in every dimension.
ER -