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

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

2011-03-08

arxiv.org/abs/1103.1451v1

SIGMA 7 (2011), 024, 16 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2011.024

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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