Generalized Heisenberg Algebras and Fibonacci Series

Details Generalized Heisenberg Algebras and Fibonacci Series Generalized Heisenberg Algebras and Fibonacci Series

2007-02-15

arxiv.org/abs/math-ph/0702053v1

Journal of Physics A: Math. Gen. 39 (2006) 10415

Physics

Mathematical Physics

24 pages, 2 figures, subfigure.sty

Scientific paper

10.1088/0305-4470/39/33/011

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.

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