**Fermi's Golden Rule** Fermi's Golden Rule:

A transition rate depends upon the strength of the coupling between the initial and final state of a system and upon the number of ways the transition can happen (i.e., the density of the final states).

T

_{i→f} = (2π/h) |M

_{if}|

^{2} ρ

_{f} δ(Ef-Ei-ħω)

where

T

_{i→f}: transition probability going from the initial to the final state. Also called the decay probability and is related to the mean lifetime t of the state by T

_{i→f} = 1/t

M

_{fi} = <f|H

_{interaction}|i> = (e/mc)<f|

**A**.

**p**|i>: the matrix element for the interaction of the initial state with the final state. The interaction Hamiltonian works on the initial state. A transition will proceed more rapidly if the coupling between the initial and final states is stronger. In the matrix element A is the (weak ; linear response is assumed) magnetic field of the optical field and p is the momentum of the electron.

ρ

_{f}: density of the final state.

δ(Ef-Ei-ħω): delta function to express that the initial and final state differ ħω in energy

The Fermi Golden Rule can be derived from perturbation theory.

See: Dresselhaus, Solid State Physics, Part II, Optical properties of solids, paragraph 3.2, page 19

__Source:__ http://en.wikipedia.org/wiki/Fermi%27s_golden_rule http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/fermi.html