Fermi's Golden Rule gives the transition rate Γ = (2π/ℏ)|⟨f|V|i⟩|² ρ(E_f) for a perturbation V coupling initial state |i⟩ to a continuum of final states |f⟩ at the same energy. It arises from first-order time-dependent perturbation theory in the limit t → ∞: the transition probability P(t) = (2/ℏ²)|V|² [sin(ΔEt/2ℏ)/(ΔE/2ℏ)]² grows linearly in time only on resonance (ΔE = 0). The sinc² function acts as an energy-selective window that sharpens to a delta function as t → ∞, enforcing energy conservation. Applications: radioactive decay, photoionization, scattering cross-sections, and relaxation in open quantum systems.