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

• URL: http://arxiv.org/abs/2106.14119v2
• Date: Wed, 20 Oct 2021 02:25:00 GMT
• Title: Ladder operators and coherent states for the Rosen-Morse system and its rational extensions
• Authors: Simon Garneau-Desroches, V\'eronique Hussin
• Abstract summary: A class of rational extensions of the RMII potential is presented and discussed. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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