A thin-layer derivation shows rotation adds a gauge field in twisted tubes, while scaling and shearing create geometric potentials that split energy degeneracies in square but not circular cross-sections.
The covariant derivative remains Ds =∂s −iτ ˆL/ℏ, and and the resulting term VH is given byVH = ℏ 2 mf∂ 1∂2
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Quantum States in Twisted Tubes with Linear Cross-Section Variation
A thin-layer derivation shows rotation adds a gauge field in twisted tubes, while scaling and shearing create geometric potentials that split energy degeneracies in square but not circular cross-sections.