|
This article is cited in 18 scientific papers (total in 18 papers)
Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
Véronique Hussina, Ian Marquetteb a Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec H3C 3J7, Canada
b Department of Mathematics, University of York, Heslington, York YO10 5DD, UK
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.
Keywords:
generalized Heisenberg algebras; degeneracies; Morse potential; infinite well potential; supersymmetric quantum mechanics.
Received: December 23, 2010; in final form March 1, 2011; Published online March 8, 2011
Citation:
Véronique Hussin, Ian Marquette, “Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential”, SIGMA, 7 (2011), 024, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma582 https://www.mathnet.ru/eng/sigma/v7/p24
|
Statistics & downloads: |
Abstract page: | 223 | Full-text PDF : | 77 | References: | 27 |
|