Exact eigenstates of a tight-binding model on a two-dimensional Penrose lattice are investigated. Several exact eigenfunctions are found for certain transfer matrices, and a method to obtain more general exact solutions is proposed. The fractal dimension of self-similar non-normalizable eigenfunctions is defined, and the characteristic of wave functions is analyzed successfully in terms of the fractal dimension.
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Tokihiro et al. (1988) studied this question.
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