Comments on Eigenvalue Problems on the Fibonacci Quasicrystals

Tomonari Dotera

(Proceedings of China-Japan seminars) Quasicrystals,
K.H.Kuo and T.Ninomiya eds. World Scientific(1991),pp.316-323


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 self-similar 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.