  We show that the 3D reductions of the Bethe-Salpeter equation have the same
bound state spectrum as the original equation, with the possible exception of
some solutions for which the corresponding 3D wave function vanishes. The
abnormal solutions of the Bethe-Salpeter equation (corresponding to excitations
in the relative time-energy degree of freedom), when they exist, are recovered
in the 3D reductions via a complicated dependence of the final potential on the
total energy. We know however that the one-body (or one high mass) limit of
some 3D reductions of the exact Bethe-Salpeter equation leads to a compact 3D
equation (by a mutual cancellation of the ladder and crossed graph
contributions), which does not exhibit this kind of dependence on the total
energy anymore. We conclude that the exact Bethe-Salpeter equation has no
abnormal solution at this limit, or has only solutions for which our 3D wave
function vanishes. This is in contrast with the results of the ladder
approximation, where no such cancellation occurs. We draw the same conclusions
for the static model, which we obtain by letting the mass of the lighter
particle go also to infinity. These results support Wick's conjecture that the
abnormal solutions are a spurious consequence of the ladder approximation.
