广义Heisenberg代数与Fibonacci级数
Generalized Heisenberg Algebras and Fibonacci Series
摘要：
我们构造了一个由哈密顿量、阶算子和一个非线性算子生成的Heisenberg型代数。这个代数描述了量子系统，其哈密顿量的本征值取决于前两个能级的本征值。例如，对于具有由斐波那契序列给出的能谱的系统，就会发生这种情况。此外，代数结构取决于两个函数f（x）和g（x）。当这两个功能是线性的，我们分类，分析稳定的不动点的功能，可能表示这个代数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
