Nonperturbative Techniques for QED Bound States
  Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics. The hydrogen atom, in the approximation of a structureless, infinite-mass nucleus, but with the leading relativistic and radiative corrections included, is used to demonstrate the construction and solution of the effective theory. The resulting Hamiltonian incorporates a finite ultraviolet cutoff and can be solved nonperturbatively. An appendix lists explicit formulae for the various matrix elements necessary to diagonalize the Hamiltonian using gaussian basis sets. 
Richard Hill