A deep inelastic neutron scattering experiment, performed on D(2)O in the stable and metastable liquid phases, provides evidence for isotope quantum effects in the proton or deuteron single particle dynamics along the hydrogen bond. The deuteron mean kinetic energy extracted from the experimental data in the metastable supercooled phase (T = 276.15 K) exceeds the zero point energy and scales as sqrt[2] with that of protons in supercooled light water, at T = 269.15 K. The present data support the suggestion that even small changes in the short range environment of a deuteron or proton have a strong influence on its quantum behavior.