Self-similar polynomials and self-similar wave functions obtained from a Fibonacci quasicrystal

Tomonari Dotera

Methods of Structural Analysis of Modulated Structures and Quasicrystals,
J.M.Perez-Mato, F.J.Zuniga and G.Madariaga eds. World Scientific (1991), pp.667-671

Recently, a new approach for studying the electronic problem of a 1-D Fibonacci quasicrystal was proposed based on transfer matrix method. The method relies on computing the trace of the transfer matrix in terms of a new set of self-similar polynomials, a quasiperiodic generalization of the Chebyshev polynomials. In this paper, we show how the method can be applied to solve for six-cycle self-similar wave functions.