Some elementary questions in the theory of quasiperiodic heterostructures

The characterization of the spectrum of eigenstates of quasiperiodic hetero structures is discussed by focusing on three questions. Arguments are advan ced to justify the often indiscriminate use of different approximants in th e calculation of;he eigenvalue spectra. It is stressed that the calculation of the fractal dimension may be rather inaccurate if the high eigenvalue r ange is not included, even if physically the interest is limited to the low range. The question of self-similarity is critically examined and found to have a very limited range of validity in practice. The unique properties o f the Rudin-Shapiro sequence are also stressed.