  The Bethe-Salpeter Equation for a bound system, composed by two massive
scalars exchanging a massive scalar, is quantitatively investigated in ladder
approximation, within the Nakanishi integral representation approach. For the
S-wave case, numerical solutions with a form inspired by the Nakanishi integral
representation, have been calculated. The needed Nakanishi weight functions
have been evaluated by solving two different eigenequations, obtained directly
from the Bethe-Salpeter equation applying the Light-Front projection technique.
A remarkable agreement, in particular for the eigenvalues, has been achieved,
numerically confirming that the Nakanishi uniqueness theorem for the weight
functions, demonstrated in the context of the perturbative analysis of the
multi-leg transition amplitudes and playing a basic role in suggesting one of
the two adopted eigenequations, can be extended to a non perturbative realm.
The detailed, quantitative studies are completed by presenting both
probabilities and Light-Front momentum distributions for the valence component
of the bound state.
