Coherent states for general potentials. III. Nonconfining one-dimensional examples

We apply our minimum-uncertainty coherent-states (MUCS) formalism to two one-dimensional systems that have continua: the symmetric Rosen-Morse potential and the Morse potential. The coherent states are discussed analytically in great detail, and the connections to annihilation-operator and displacement-operator coherent states are given. For the Rosen-Morse system the existence of a continuum does not prevent one from obtaining the coherent states in analytic, closed form. The Morse system, with its energy-dependent natural classical variable $X_c$, has a natural quantum operator $X$ which is Hamiltonian-dependent. This Hamiltonian dependence is complicated and prevents an easy analytic solution for the MUCS. However, approximate MUCS can be obtained by analytic approximation techniques.