Comments on Eigenvalue Problems on the Fibonacci Quasicrystals We review our recent development for electronic problems on the Fibonacci quasicrystal. Our method relies on transfer matrix method in terms of a new set of selfsimilar polynomials, a quasiperiodic generalization of the Chebyshev polynomials of the first kind. We discuss physical meaning with recourse to the polynomials, which clarifies the relation between the lattice and spectrum. 
