Forest FermiGoldenRule Notes

Fermi's Golden rule is used to calculate the probability (per unit time) of a quantum mechanical transition between two quantum states. Although Fermi first coined the term "Golden Rule", Dirac developed most of the machinery.

$| M_{i,f}| ^2 = \int \psi_i^{*} H_{pert} \psi_f dv$

where

$\psi_i$ = initial quantum state of the system

$\phi_f$ = final quantum state of system after a transition

$H_{pert}$ = part of the Hamiltonian which is responsible for the transition.

$H_0$ = Unperturbed ("steady state") Hamiltonian

$H_{tot} = H_0 + H_{pert}$ = total hamiltonian describing the quantum mechanical system

$dv$ integration over all space