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

TL;DR

This paper constructs ladder operators and coherent states for the Rosen-Morse potential and its rational extensions, utilizing shape invariance and supersymmetric quantum mechanics, and extends these concepts to the trigonometric case.

Contribution

It introduces a method to realize ladder operators for rational extensions of the Rosen-Morse potential and constructs associated coherent states, extending the framework to the trigonometric case.

Findings

Ladder operators are explicitly constructed for rational extensions.

Coherent states are formed as almost eigenstates of the lowering operators.

The approach is extended from hyperbolic to trigonometric Rosen-Morse potentials.

Abstract

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.