Explicit construction of Floquet–Bloch states from arbitrary solution bases of the Hill equation
Abstract
Abstract For the Hill equation describing one-dimensional periodic systems, an explicit construction of Floquet–Bloch states from arbitrary pairs of linearly independent solutions is developed. Closed-form formulas map an arbitrary fundamental system to a Floquet–Bloch basis via the monodromy matrix, including the generic Jordan band-edge case, without reliance on canonically normalized solutions. An equivalent transfer-matrix formulation makes the residual representation freedom transparent and provides a practical framework for analytical and numerical studies of periodic systems.
Fields of Study & Subjects
Quantum Mechanics and Non-Hermitian Physics
Quantum chaos and dynamical systems
Topological Materials and Phenomena
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Publisher
- IOP Publishing
- Volume
- 59
- Issue
- 14
- Pages
- 145206–145206
- Publication date
- 2 April 2026
- Language
- EN