Fermi's Golden Rule
In quantum physics, Fermi's golden rule is a simple formula for the constant transition rate (probability of transition per unit time) from one energy eigenstate of a quantum system into other energy eigenstates in a continuum, effected by a perturbation. This rate is effectively constant.
Although named after Enrico Fermi, most of the work leading to the Golden Rule is due to Paul Dirac who formulated 20 years earlier a virtually identical equation, including the three components of a constant, the matrix element of the perturbation and an energy difference. It was given this name because, on account of its importance, Fermi dubbed it "Golden Rule No. 2."
Consider the system to begin in an eigenstate, , of a given Hamiltonian, H0 . Consider the effect of a (possibly time-dependent) perturbing Hamiltonian, H' . If H' is time-independent, the system goes only into those states in the continuum that have the same energy as the initial state. If H' is oscillating as a function of time with an angular frequency ω, the transition is into states with energies that differ by ħω from the energy of the initial state.
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