Explicit closed-form formulas map arbitrary fundamental solutions of the Hill equation to Floquet-Bloch states via the monodromy matrix, including Jordan band-edge cases.
We first treat the generic diagonalizable case, characterized by tr[ ˜A] ≡ a11 + a22 ̸= ± 2, for which the multipliers satisfy ρ1 ̸= ρ2
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2026 1verdicts
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Explicit Construction of Floquet-Bloch States from Arbitrary Solution Bases of the Hill Equation
Explicit closed-form formulas map arbitrary fundamental solutions of the Hill equation to Floquet-Bloch states via the monodromy matrix, including Jordan band-edge cases.