处于边缘的量子系统：原子束缚态在电离阈值处的性质
Quantum Systems at The Brink: Properties of Atomic Bound States at The Ionization Threshold
摘要：
我们给出了一个严格的论点，长程排斥稳定的量子系统，这样的量子系统的基态存在，即使当基态能量正好在电离阈值。对于处于临界核电荷的原子系统，我们的边界表明，对于大的$|x|$，基态像$\exp(-c\sqrt{|x|})$一样下降。这比WKB方法预测的能量严格低于电离阈值的束缚态要慢得多。对于临界核电荷的氦型系统，我们证明了我们的上界是尖锐的。这严格证实了量子化学家的预测。
英文摘要：
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.
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