An su(1,1) dynamical algebra for the Morse potential

An su (1, 1) dynamical algebra to describe both the discrete and the continuum parts of the spectrum for the Morse potential is proposed. The space associated with this algebra is given in terms of a family of orthonormal functions {Phi(n)(sigma)} characterized by the parameter sigma. This set is constructed from polynomials which are orthogonal with respect to a weighting function related to a Morse ground state. An analysis of the associated algebra is investigated in detail. The functions are identified with Morse-like functions associated with different potential depths. We prove that for a particular choice of or the discrete and the continuum parts of the spectrum decouple. The connection of this treatment with the supersymmetric quantum mechanics approach is established. A closed expression for the Mecke dipole moment function is obtained.