  The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby
reducing the original 4-dimensional integral equation into an infinite set of
coupled 1-dimensional ones. It is shown that this representation offers a
highly accurate method to determine numerically the bound state solutions. For
generic cases only a few hyperspherical waves are needed to achieve
convergence, both for the ground state as well as for radially or orbitally
excited states. The wave function is reconstructed for several cases and in
particular it is shown that it becomes independent of the relative time in the
nonrelativistic regime.
