On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall,and the Absence of Embedded Eigenvalues

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(2Z - )mc², where 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 3/4 . Implications for the operators in the partial wave decomposition are also described.