关于Brown和Ravenhall相对论性算子的维里定理及无嵌入本征值
On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues
摘要：
本文对Brown和Ravenhall提出的相对论单电子原子模型建立了维里定理。因此，它被证明，运营商没有本征值大于$\max(m c^2, 2 αZ - \frac{1}{2})$，其中$α$是精细结构常数，所有的值的核电荷$Z$低于临界值$Z_c$：特别是没有本征值嵌入在本质谱时，$Z \leq 3/4 α$。在分波分解的运营商的影响也被描述。
英文摘要：
A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than $\max(m c^2, 2 αZ - \frac{1}{2})$, where $α$ is the fine structure constant, for all values of the nuclear charge $Z$ below the critical value $Z_c$: in particular there are no eigenvalues embedded in the essential spectrum when $Z \leq 3/4 α$. Implications for the operators in the partial wave decomposition are also described.
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