Neutron Compton scattering measurements presented here of the momentum distribution of hydrogen in $\mathrm{K}{\mathrm{H}}_{\mathrm{2}}\mathrm{P}{\mathrm{O}}_{\mathrm{4}}$ just above and well below the ferroelectric transition temperature are sufficiently sensitive to show clearly that the proton is coherent over both sites 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.

• Received 7 March 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.135505