title: Deriving exact energy solutions to the symmetrized q-difference Harper equation.
abstract: This paper deals with the application of the q calculus to second order q-difference equations, like the q symmetrized form of the Harper equation. One obtains three-term recurrence relations, for which a symmetrized version is written down. This opens the way to establish explicit energy results that are dependent on the commensurability parameter. The continuous realization of such energy results exhibits interesting patterns characterized by hierarchical structures.
authors: Physics Department, North University of Baia Mare, RO-4800 Baia Mare, Romania. epapp@arad.ro
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authors: Papp
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authors: Micu