Sharp eigenvalue bounds on quantum star graphs

Abstract

We prove that the optimal constant in the Lieb--Thirring inequality on a star graph with $N$ edges coincides with that on $\mathbb{R}$ if $N$ is even. For odd $N$ we show that this property holds when restricting to radial potentials and we prove an almost optimal bound for general potentials.

10 pages

Cited by in corpus (1)

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