  We investigate the overlap of the ground state meson potential with sets of
mesonic-trial wave functions corresponding to different gluonic distributions.
We probe the transverse structure of the flux tube through the creation of
non-uniform smearing profiles for the string of glue connecting two color
sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube
operators are found to optimize the overlap with the ground state and display
interesting features in the ground state overlap.
