The quantum lifetime of the Davydov soliton

Considering an infinite spine in the Alpha-helix, stationary states should be eigenstates of a translational operator. These states should be nonlocalized in contradiction to a localized soliton. The difference in energy between localized and nonlocalized (Bloch) states is due to zero point motion and gives information about the quantum stability of the Davydov soliton. We develop a theory of statinary states and show that only for the limiting case of a classical lattice the product ansatz by Davydov is exact. Finally, we calculate the width of the soliton band to get information on the lifetime of the localized soliton.