A variational approach to the eigenfunctions of the one particle relativistic Hamiltonian

In this note we give a variational characterization of the eigenvalues and eigenvectors for the relativistic (free) Hamiltonian operator with a real valued potential. Our results hold for Coulomb-type potential V. The characterization we give for the eigenvectors is useful in proving regularity and exponential decay of the solutions — properties which have been object of investigation by B. Simon with different techniques.