A variational approach to the Brown–Ravenhall operator for the relativistic one-electron atoms

Abstract

We study the Brown–Ravenhall operator (the projection of the Dirac operator perturbed by a potential V∈Lw3) using the Foldy–Wouthuysen (unitary) transformation and its realization as an elliptic problem in the 4-dim half space R+4 with Neumann boundary condition. Using this approach we give a characterization of its eigenvalues and eigenfunctions alternative to the classical Rayleigh quotients.