Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
Copyright policy )Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
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.
- University of Montreal Canada
- Department of Mathematics University of York United Kingdom
- University of York United Kingdom
Operator algebra methods applied to problems in quantum theory, degeneracies, supersymmetric quantum mechanics, Quantum Physics, infinite well potential, Generalized Heisenberg algebras, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Degeneracies, Infinite well potential, Supersymmetric field theories in quantum mechanics, QA1-939, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, generalized Heisenberg algebras, Morse potential, Quantum Physics (quant-ph), Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematics, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis
Operator algebra methods applied to problems in quantum theory, degeneracies, supersymmetric quantum mechanics, Quantum Physics, infinite well potential, Generalized Heisenberg algebras, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Degeneracies, Infinite well potential, Supersymmetric field theories in quantum mechanics, QA1-939, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, generalized Heisenberg algebras, Morse potential, Quantum Physics (quant-ph), Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematics, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis
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