Inelastic neutron scattering studies of some hydrogen bonded crystals (e.g., potassium hydrogen carbonate, KHCO 3) have revealed that the dynamics of protons is largely decoupled from the lattice. The KHCO 3 crystal is a prototypical system for proton dynamics which contains centro-symmetric dimer entities (HCO 3-) 2 linked by moderately strong hydrogen bonds. The quantum dynamics of pairs of coupled oscillators is analyzed. It is shown that the Pauli principle applied to normal coordinates for fermions gives new quantum properties in the degenerate ground state. Vibrational wave functions for the singlet and triplet states are derived. A new spin-related selection rule in proposed: the dynamics of fermions (e.g., H atoms) is decoupled from the dynamics of bosons (e.g., C and O atoms). Scattering functions for the protons are calculated with various models: the single harmonic oscillator, the double minimum potential and pairs of coupled harmonic oscillators. It is concluded that quantum interferences should be observed with elastic neutron scattering for pairs of coupled fermions.