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On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2

Timo Weidl
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Abstract

Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb R})$. We prove the inequality \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb R} V^{\gamma+1/2}(x)dx, (1) for the "limit" case $\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\gamma,1}$ in (1), as $1/2<\gamma<3/2.

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Timo Weidl. 1995-04-17. On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2. https://doi.org/10.1007/bf02104912

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