On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues

Details On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues

1998-02-06

arxiv.org/abs/math/9802035v1

Mathematics

Spectral Theory

To appear in Letters in Math. Physics

Scientific paper

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 $\max(m c^2, 2 \alpha Z - \frac{1}{2})$, where $\alpha$ 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 $Z \leq 3/4 \alpha$. Implications for the operators in the partial wave decomposition are also described.

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