On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall, and the Absence of Embedded Eigenvalues
نویسنده
چکیده
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(mc, 2αZ− 1 2 ), 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 ≤ 3/4α. Implications for the operators in the partial wave decomposition are also described.
منابع مشابه
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