arXiv · math/9802035
On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues
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 $\max(m c^2, 2 αZ - \frac{1}{2})$, 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.
Explore related subjects
Keep this discovery
A. A. Balinsky, W. D. Evans. 1998-02-06. On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues. https://arxiv.org/abs/math/9802035
Cite the original work for its findings. Save a collection to share your selection of sources.