%0 Journal Article
%T A variational approach to the Brown-Ravenhall operator for the relativistic one-electron atoms
%A Vittorio Coti Zelati
%A Margherita Nolasco
%J Mathematics
%D 2014
%I arXiv
%X We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In particular we transform the eigenvalues problem into an elliptic problem in the 4-dim half space $\mathbb{R}^4_{+}$ with Neumann boundary condition.
%U http://arxiv.org/abs/1405.4656v1