Ladder operators and coherent states for the Rosen-Morse system and its rational extensions

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.

Automated summary

Ladder operators for the hyperbolic Rosen-Morse (RMII) potential are realized using the shape invariance property and extended to a specific class of rational extensions. Coherent states are constructed as almost eigenstates of the lowering operators. The constructions are extended to the case of the trigonometric Rosen-Morse (RMI) potential using a point canonical transformation.