Series solution of the Schroumldinger equation with the Morse potential

An analytic series solution to the Schroedinger equation with the Morse potential has been obtained. In the present solution the Morse potential itself is also expanded in a series about the origin. For application to the problem of the density dependence of muon-catalyzed d-t fusion, the effective two-body molecular problem is also formulated in terms of the superimposed potential field inside a liquid cell due to nearest-neighbor molecules (atoms). In this approach, more detailed studies can be carried out of the density effect on the various matrix elements needed in the calculations of the rates of μ-meson d-t fusion