The distributions of the quantum vibrational energy levels of the protein m
olecular chain are found by the discretely nonlinear Schrodinger equation a
ppropriate to protein obtained from the Davydov theory. The results calcula
ted by this method are basically consistent with the experimental values. F
urthermore, the energy spectra at high excited states have also been obtain
ed for the molecular chain which is helpful in researching the properties o
f infrared absorption and Raman scattering of the protein molecules.