  Neutron Compton Scattering measurements presented here of the momentum
distribution of hydrogen in $KH_2PO_4$ (KDP) just above and well below the
ferroelectric transition temperature show clearly that the proton is coherent
over both sites in the in the high temperature phase, a result that invalidates
the commonly accepted order-disorder picture of the transition.
  The Born-Oppenheimer potential for the hydrogen, extracted directly from data
for the first time, is consistent with neutron diffraction data, and the
vibrational spectrum is in substantial agreement with infrared absorption
measurements. The measurements are sensitive enough to detect the effect of
surrounding ligands on the hydrogen bond, and can be used to study the
systematic effect of the variation of these ligands in other hydrogen bonded
systems.
