title: Interplays between Harper and Mathieu equations.
abstract: This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.
authors.affiliation: Department of Physics, North University of Baia Mare, Strasse Victoriei 76, RO-4800, Baia Mare, Romania. epapp@arad.ro
authors.forename: E
authors.initials: E
authors.lastname: Papp
authors.forename: C
authors.initials: C
authors.lastname: Micu