Fermi's golden rule

Fermi's golden rule gives the transition rate between quantum states under a weak perturbation. The rate is proportional to the squared transition matrix element and the density of energetically allowed final states.

Time-dependent perturbation theory: A framework for calculating how time-varying interactions change quantum states. The rule emerges when first-order transition amplitudes are evaluated at long times.
Fermi's theory of beta decay: Enrico Fermi's theory describing beta decay as a weak interaction that emits an electron and a neutrino. The golden rule converts the weak interaction matrix element into a decay rate.
Enrico Fermi: An Italian-born physicist whose work shaped nuclear, particle, and statistical physics. The rule bears his name and was developed in his treatment of transition processes.
Rabi oscillation: Coherent periodic transfer of population between two quantum states driven by an oscillating field. A discrete resonant pair oscillates coherently rather than decaying at a constant golden-rule rate.
Non-Markovian quantum dynamics: Quantum evolution with memory effects, in which future dynamics depend on past system-environment interactions. Environmental memory can make transition rates time-dependent rather than golden-rule constants.
Transition matrix element: A quantum amplitude measuring how an operator couples an initial state to a final state. Its squared magnitude sets the transition strength in the rule.
Spontaneous emission: The emission of a photon by an excited atom without an applied electromagnetic field. Coupling to vacuum electromagnetic modes gives an atomic decay rate through the rule.
Quantum mechanics: A physical theory describing matter and radiation through states, observables, and probabilistic measurement outcomes. The rule is a result within quantum mechanics, not a classical rate law.
Fermi's golden rule for strong coupling: A regime in which transition dynamics cannot be reliably approximated by the weak-coupling golden rule. Strong interactions invalidate the rule's perturbative assumption and can reshape the states.
Wigner-Weisskopf approximation: An approximation for the decay of an unstable quantum state coupled to a continuum of states. It extends golden-rule reasoning to exponential decay while revealing approximations behind that rate.

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