An analysis of the quantum mechanical relativistic two-body problem

A 16 x 16 relativistic two-body equation has been derived from field theory. This equation is a one time equation and it has all the recoil and spin effects of both Dirac particles. The equation is separable to center of mass and relative motions. The relative motion is separable to radial and angular parts. The 16 radial-coupled first-order differential equations reduce to two sets of eight equations. Each set is reduced to two coupled second-order differential equations on two radial functions. The second-order differential equations are approximated to order α4 and the exactly solvable parts are solved. The results of the energy eigenvalues up to order α4 are the same as the standard theory