In quantum physics, Fermi’s golden rule is used to calculate transition rates. The transition rate depends upon the strength of coupling between the initial and final state of a system and upon the number of ways the transition can happen (joint density of states). The transition probability is given by: λif = 2πℏ Mif 2 Zf Where, λif is transition probability, Mif 2 is matrix element for interaction and Zf is joint density of final state. The above equation is known as fermi’s golden rule. The transition probability λ is called the decay probability and is related to mean lifetime τ of the state. λ = 1τ The general form of fermi’s golden rule can be applied to atomic transitions. Nuclear decay and scattering. This coupling term is traditionally called the matrix element for the transition. This matrix element can be placed in the form of an integral, where the interaction (that causes transition) is expressed as a potential v that operates on initial state wave function. The transition probability is proportional to the square of integral of interaction over all of the space appropriate to the problem. Mif = ∫ψ*f · V · ψ i ·dv Where, V is operator for physical interaction that couples initial and final states, ψ*f is wave function for final state and ψ i is wave function for initial state.
