论文标题
边缘处的量子系统：在电离阈值处原子结合状态的特性
Quantum Systems at The Brink: Properties of Atomic Bound States at The Ionization Threshold
论文作者
论文摘要
我们提出了一个严格的论点，即长距离排斥稳定量子系统。即使基态能恰好处于电离阈值，这种量子系统的基态也存在。对于关键核电的原子系统，我们的边界表明，基态掉落，例如$ \ exp（-c \ sqrt {| x |}）$，对于大$ | x | $。这比WKB方法对结合状态的预测慢得多，其能量严格低于电离阈值。对于关键核电的氦类型系统，我们表明我们的上限是锋利的。这严格证实了量子化学家的预测。
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the ionization threshold. For atomic systems at the critical nuclear charge, our bounds show that the ground state falls off like $\exp(-c\sqrt{|x|})$ for large $|x|$. This is much slower than what the WKB method predicts for bound states with energies strictly below the ionization threshold. For helium type systems at critical nuclear charge, we show that our upper bounds are sharp. This rigorously confirms predictions by quantum chemists.
