Work

Explicit construction of Floquet–Bloch states from arbitrary solution bases of the Hill equation

Year: 2026

Type: article

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.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ae5aff

Author: Gregory V Morozov

Institutions: Scottish Universities Physics Alliance, University of the West of Scotland

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

OpenAlex ID: W7148454069

FWCI: 11.39

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Cited by: 1

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