The Bogoliubov transformation mixes electron and hole states: γₖ = uₖcₖ↑ + vₖc†₋ₖ↓. This creates quasiparticle excitations with energy Eₖ = √(ξₖ² + Δ²), gapped by the pairing amplitude Δ. Adjust chemical potential μ and gap Δ to see the dispersion, coherence factors, and density of states.