A variational approach to the Brown-Ravenhall operator for the   relativistic one-electron atoms
  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. 
Vittorio Coti Zelati and Margherita Nolasco
math.AP math-ph math.MP