Generalized Heisenberg Algebras and Fibonacci Series

Abstract

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.

24 pages, 2 figures, subfigure.sty

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Cited by in corpus (9)

• Pisot q-Coherent states quantization of the harmonic oscillator
• Generalized Heisenberg algebras and k-generalized Fibonacci numbers
• Quasi-Fibonacci oscillators
• Polynomially deformed oscillators as k-bonacci oscillators
• Intermediate statistics: addressing the thermoelectric properties of solids
• Modeling amortization systems with vector spaces
• Quantum credit loans
• Intermediate statistics: addressing the Landau diamagnetism problem
• Finite-dimensional simple modules over generalized Heisenberg algebras