  The N-quantum approach (NQA) to quantum field theory uses the complete and
irreducible set of in or out fields, including in or out fields for bound
states, as standard building blocks to construct solutions to quantum field
theories. In particular, introducing in (or out) fields for the bound states
allows a new way to calculate energy levels and wave functions for the bound
states that is both covariant and effectively 3-dimensional. This method is
independent of the Bethe-Salpeter equation. In contrast to the Bethe-Salpeter
equation, all solutions of the NQA are normalizable and correspond to physical
bound states. In this paper we use the NQA in one-loop approximation to
calculate states of the relativistic hydrogen atom and analogous two-body
systems to illustrate how our new method works. With additional terms in the in
field expansion we find systematic corrections beyond the Coulomb interaction.
