  A non-covariant but approximately relativistic two-body wave equation (Breit
equation) describing the quantum mechanics of two fermions interacting with one
another through a potential containing scalar, pseudoscalar and vector parts is
presented. After expressing the sixteen component two-body wavefunction in
terms of a radial and an angular function by means of the multipole expansion,
the initial equation can be reduced into a set of sixteen radial equations
which, in turn, can be classified in accordance to the parity and the state of
the wavefunctions involved. The adequacy of the reduced equations in describing
real problems is discussed by applying the theory to QCD problems and the
calculation of the energies of bound states of quark-antiquark systems is
performed to order $\alpha^4$. We show that bound states of heavy quarks can be
described adequately by the Breit equation for a funnel interaction between the
particles
