Amplitude-phase method for solving Floquet-type problems

Abstract

Abstract The understanding of one-dimensional quantal and dynamical problems is fundamental to problems involving stability of material constructions, quantum tunneling in solids, chemical selection of gas components, electronic properties of material nanostructures. An amplitude-phase method for one-dimensional Schrödinger/Hill-type equations with periodic potentials/coefficients is shown to provide detailed insights into Floquet-type quantal and dynamical problems. Method-independent real and periodic local amplitude and wave-number (or angular frequency) functions are found for bounded Floquet solutions. Regular and weakly singular periodic potentials/coefficients of analytic forms apply.