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This lecture delves into the derivation of band structures in semiconductors, focusing on the selection of reciprocal wave vectors and the impact of different periodicities on band shapes. The instructor explains how the choice of vectors affects the band structure and clarifies why specific solutions are considered for materials like silicon. Additionally, the discussion extends to the coupling of electron and phonon vibrations in the lattice, addressing the implications of assuming stationary ionic cores and the negligible deviation when considering phonon modes in the derivation.