  We analyze the equal-time Bethe-Salpeter quark wave functions of the pion in
various models. We discuss how the quenched lattice QCD results with
delocalized pion interpolators can be identified with the coarse grained wave
functions, typical of low-energy effective models. Actually, we find that
one-loop chiral quark models predict that pseudoscalar and tensor wave
functions have the same shape, while the axial component is more extended.
These facts are accurately confirmed by the lattice. We also show how the
transversity information, relevant for the light-cone physics, can be
straightforwardly obtained from the equal-time rest-frame lattice calculations.
This remarkable relation provides a way to extract, for instance, the
equal-time holographic wave functions and compare them, quite favorably, to the
lattice calculations.
