  Scalar Fields (SF) have emerged as natural candidates for dark energy as
quintessential or phantom fields, as they are the main ingredient of inflation
theories. Instead of assuming some form for the scalar field potential,
however, this work reconstructs the SF potential directly from observational
data, namely, \textbf{Hubble and SNe Ia data}. We show that two popular forms
for the SF potentials, namely, the power-law and the quadratic free-field, are
compatible with the reconstructions thus obtained, at least for some choices of
the priors of the matter density and curvature parameters and for some redshift
intervals.
