  Ladder operators for the hyperbolic Rosen-Morse (RMII) potential are realized
using the shape invariance property appearing, in particular, using
supersymmetric quantum mechanics. The extension of the ladder operators to a
specific class of rational extensions of the RMII potential is presented and
discussed. Coherent states are then constructed as almost eigenstates of the
lowering operators. Some properties are analyzed and compared. The ladder
operators and coherent states constructions presented are extended to the case
of the trigonometric Rosen-Morse (RMI) potential using a point canonical
transformation.
