相对论强斯科特猜想:一个简短的证明

arXiv: Mathematical Physics Pub Date : 2020-09-05 DOI:10.1142/9789811272158_0003

R. Frank, Konstantin Merz, H. Siedentop

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引用次数: 5

摘要

我们考虑原子序数为$Z$的重中性原子，用钱德拉塞卡已经使用过的动能$(c^2p^2+c^4)^{1/2}-c^2$来建模。在保持$Z/c$固定的极限$Z,c\to\infty$下，我们研究了单粒子基态密度在长度尺度$Z^{-1}$上的行为。我们给出了作者和Barry Simon最近的一个结果的简短证明，该结果表明密度在这个尺度上收敛于相对论性的氢密度。

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Relativistic Strong Scott Conjecture: A Short Proof

We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the limit $Z,c\to\infty$ keeping $Z/c$ fixed. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale.

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arXiv: Mathematical Physics

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