Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential

Abstract

We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.

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• The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
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• Robustness of deformed catlike states under dissipative decoherence
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions