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

Symmetry Integrability and Geometry-Methods and Applications

article

Véronique Hussin¹  Ian Marquette² 

[1] Département de mathématiques et de statistique, Université de Montréal;Department of Mathematics, University of York

关键词: generalized Heisenberg algebras;    degeneracies;    Morse potential;    infinite well potential;    supersymmetric quantum mechanics;   

DOI  :  10.3842/SIGMA.2011.024

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown