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Fermi Golden Rule

A mathematical rule that describes the transition rate between quantum states in a perturbed system, frequently applied to nuclear transitions.
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The statement of the theorem

For a transition from an initial state ∣i⟩|i\rangle to a final state ∣f⟩|f\rangle induced by a perturbation H′\mathcal{H}', the transition rate Γi→f\Gamma_{i \to f} is given by Fermi's Golden Rule:\nΓi→f=2Im(⟨f∣H′∣i⟩))ℏρ(Ef)\Gamma_{i \to f} = \frac{2\text{Im}(\langle f | \mathcal{H}' | i \rangle))}{\hbar} \rho(E_f) \nwhere ⟨f∣H′∣i⟩\langle f | \mathcal{H}' | i \rangle is the matrix element of the perturbation, and ρ(Ef)\rho(E_f) is the density of final states at the energy EfE_f.
Source: Wikipedia