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Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
Інший ID:
2010 Mathematics Subject Classification: 81R15; 81R12; 81R50
DOI:10.3842/SIGMA.2011.024
DOI:10.3842/SIGMA.2011.024
Посилання:
Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential / V. Hussin, I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
The research of I. Marquette was supported by a postdoctoral research fellowship from FQRNT of Quebec. V. Hussin acknowledge the support of research grants from NSERC of Canada. Part of this work has been done while V. Hussin visited Northumbria University (as visiting professor and sabbatical leave).
Дата:
2011
Переглядів:
658
Завантажень:
277
Анотація:
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.
