Abstract
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(2αZ - \( \frac{1}{2} \))mc2, where α is the fine structure constant, for all values of the nuclear charge Z below the critical value Zc: in particular, there are no eigenvalues embedded in the essential spectrum when Z ≤ 3/4 α. Implications for the operators in the partial wave decomposition are also described.
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Balinsky, A., Evans, W.D. On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall, and the Absence of Embedded Eigenvalues. Letters in Mathematical Physics 44, 233–248 (1998). https://doi.org/10.1023/A:1007425400991
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DOI: https://doi.org/10.1023/A:1007425400991