dorsal/arxiv
View SchemaOn the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2
| Authors | Timo Weidl |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9504013 |
| URL | https://arxiv.org/abs/quant-ph/9504013 |
| DOI | 10.1007/BF02104912 |
| Journal | Commun.Math.Phys. 178 (1996) 135-146 |
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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"abstract": "Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional\nSchr\\\"odinger operator $Hu:=-u^{\\prime\\prime}-Vu,\\ V\\geq 0,$ on $L_2({\\Bbb\nR})$. We prove the inequality \\sum_i|E_i(H)|^\\gamma\\leq L_{\\gamma,1}\\int_{\\Bbb\nR} V^{\\gamma+1/2}(x)dx, (1) for the \"limit\" case $\\gamma=1/2.$ This will imply\nimproved estimates for the best constants $L_{\\gamma,1}$ in (1), as\n$1/2\u003c\\gamma\u003c3/2.",
"arxiv_id": "quant-ph/9504013",
"authors": [
"Timo Weidl"
],
"categories": [
"quant-ph",
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"math.FA"
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"doi": "10.1007/BF02104912",
"journal_ref": "Commun.Math.Phys. 178 (1996) 135-146",
"title": "On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2",
"url": "https://arxiv.org/abs/quant-ph/9504013"
},
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