重原子的基态能量：相对论降低的主导能量修正
The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
摘要：
我们用一个伪相对论模型来描述原子，这个模型起源于Eschrasekhar的工作。我们证明了重原子的主导能量修正--Scott修正是存在的。它比原子的非相对论描述要低。我们的证明是有效的，包括临界耦合常数。它是基于能量的重整化，我们将其零能级调整为相应的非相对论问题的基态能量。这使我们能够通过相对简单的技术手段将证明回滚到薛定谔算子的结果。
英文摘要：
We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the non-relativistic description of atoms. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This allows us to roll the proof back -- by relatively simple technical means -- to results for the Schrödinger operator.
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