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利用单电子、紧束缚、最近邻座模型 ,在重整化群的基础上 ,用分解 消元法分析了二维单原子斐波那契类准晶FC(n)的电子能谱分裂规律 ,数值计算了其电子能谱值 ,发现在一级近似下 ,该类二维准晶格中全部都只存在n×n ,n× (n + 1) ,(n + 1)× (n + 1)等三种原子簇分子 ,相应的能谱按Ym -n -l方式分裂 ,得出了其电子能谱的能级数目通式 ,发现描述其能级数目的参量存在所谓的“斐波那契类数集合” ,并且确定了该集合的前 11个整数的稳定值 ,找出了有关斐波那契类数集合的经验公式 .分析结果与数值计算值相符
Based on the renormalization group, the electronic energy splitting law of the two-dimensional monatomic Fibonacci quasicrystal FC (n) was analyzed by decomposing elimination method, using single electron, tight binding and nearest neighbor model. The numerical values of the electron spectra were numerically calculated and found that in the first-order approximation only n × n, n × (n + 1), (n + 1) × (n + 1 ) And other three cluster molecules, the corresponding energy spectrum by Ym-n-way split, the energy level of the electronic spectrum obtained by the general formula, the number of energy level description of the description of the existence of the so-called “Fibonacci Set of class numbers ”, and the stability values of the first eleven integers of the set are determined, and the empirical formula of the Fibonacci class number set is found. The analysis result is consistent with the numerical value