Almost Periodic Schrgdinger Operators Iv. the Maryland Model*

Exactly solvable models are useful laboratories that can teach one both positive and negative lessons: Certain phenomena that one might not expect or about which one might be unsure can be examined, while, on the other hand, one can find explicit counterexamples to “reasonable” conjectures. Of course, one must decide which aspects of the model are typical and which are artifacts of its special elements. Thus the discovery of an exactly solvable almost periodic Schradinger operator by Grempel, Fishman and Prange [ 19,301 (henceforth GFP) is very significant. It is their model, which we dub the Maryland model, that we wish to study here. The basic model is the Jacobi matrix (= discrete Schriidinger operator) on I’(Z):