Fermi golden rule

E914952

physical law quantum mechanical formula transition rate formula

The Fermi golden rule is a fundamental quantum mechanical formula that gives the transition rate between energy states due to a weak perturbation, widely used to describe processes like spontaneous emission and scattering.

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All labels observed (3)

Label	Occurrences
Fermi golden rule canonical	1
Fermi’s golden rule	1
Fermi’s golden rule in many-body theory	1

How this entity was disambiguated

This entity first appeared as the object of triple T11265309 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Fermi golden rule
Context triple: [Purcell effect, relatedTo, Fermi golden rule]

A. Landau–Zener formula
The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
B. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
C. Einstein coefficients
Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
D. Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
E. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Fermi golden rule
Target entity description: The Fermi golden rule is a fundamental quantum mechanical formula that gives the transition rate between energy states due to a weak perturbation, widely used to describe processes like spontaneous emission and scattering.

A. Landau–Zener formula
The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
B. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
C. Einstein coefficients
Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
D. Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
E. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	physical law ⓘ quantum mechanical formula ⓘ transition rate formula ⓘ
appliesTo	weak perturbations ⓘ
approximationType	first-order approximation ⓘ
assumes	continuum of final states ⓘ weak coupling between initial and final states ⓘ
basedOn	time-dependent perturbation theory ⓘ
describes	transition rate between quantum states ⓘ
expresses	probability per unit time of a transition ⓘ
field	quantum mechanics ⓘ theoretical physics ⓘ
hasForm	transition rate proportional to \|⟨f\|V\|i⟩\|² ρ(Ef) ⓘ
historicalPeriod	20th century ⓘ
involvesQuantity	Dirac delta function for energy conservation ⓘ squared modulus of the matrix element ⓘ
namedAfter	Enrico Fermi ⓘ
relatedTo	Born approximation ⓘ linked to: Born approximation in scattering theory Einstein A coefficient ⓘ linked to: Einstein coefficients Einstein B coefficients ⓘ linked to: Einstein coefficients Fermi’s golden rule in many-body theory ⓘ linked to: Fermi golden rule S-matrix theory ⓘ linked to: S-matrix
relates	transition rate to density of final states ⓘ transition rate to matrix element of perturbation ⓘ
symbolUses	density of states ρ(E) ⓘ final state \|f⟩ ⓘ initial state \|i⟩ ⓘ perturbation operator V ⓘ
usedFor	decay processes ⓘ electron-phonon interactions ⓘ nuclear decay rates ⓘ optical absorption ⓘ phonon scattering ⓘ scattering processes ⓘ spontaneous emission ⓘ stimulated emission ⓘ transition probabilities in atoms ⓘ transition probabilities in molecules ⓘ transition probabilities in solids ⓘ tunneling transitions ⓘ
usedIn	atomic physics ⓘ condensed matter physics ⓘ molecular physics ⓘ nuclear physics ⓘ particle physics ⓘ quantum optics ⓘ solid-state physics ⓘ
validWhen	first-order perturbation theory is adequate ⓘ perturbation is time-independent or slowly varying ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Purcell effect → relatedTo → Fermi golden rule ⓘ

Kramers–Heisenberg dispersion formula → relatedTo → Fermi’s golden rule ⓘ

linked to: Fermi golden rule

Fermi golden rule → relatedTo → Fermi’s golden rule in many-body theory ⓘ