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Treatment Of A Ring With Periodic Atomic Placement Through Differential Geometry, Gregory Karjala, Lok Lew Yan Voon
Treatment Of A Ring With Periodic Atomic Placement Through Differential Geometry, Gregory Karjala, Lok Lew Yan Voon
Explorations – The Journal of Undergraduate Research, Scholarship and Creativity at Wright State
Most treatments of Bloch’s Theorem have relied on group theory or other mathematical methods for its proof. In this paper we give a derivation of the quantum number first proposed by Y.C Lee and Wei Z. Lee for the Benzene ring through the use of differential geometry. We also develop a Bloch style relationship relation for the benzene ring with an additional quantum number. Through this treatment we show the usefulness of differential geometry in the theorist’s toolkit when it comes to solid-state problems.