The Compton profiles (CP) of H:('Z,') are calculated using the exact Born-Oppenheimer (BO) wavefunction for various internuclear distances R. By using the rotational-vibrational ( RV) state distribution factors, calculated according to the Franck-Condon ( FC) principle or measured from experiment, the vibrationally averaged values of C P for H;('L,') and D;(2Zl) in the adiabatic approximation are also calculated. Various theoretical values are given for comparison with the CP measured from H;-Ar collisions. The experimental data are most compatible with the exact BO values at R = 2.0 au but the data, with an error of IS%, fail to resolve various theoretical values at either small or large momenta q. It is important to have accurate experimental data (of absolute measurements) with an error of less than 10% in order to determine the accuracy of the theoretical values reported here.