Remarks on the spectral properties of tight-binding and Kronig-Penney models with substitution sequences

We comment on some recent investigations on the electronic properties of models associated with the Thue-Morse chain, point out that their conclusions contradict rigorously proven theorems, and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.