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Fermi's Golden Rule (Read 2258 times)
Gerrit-Jan Linker
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Fermi's Golden Rule
18.07.12 at 07:43:16
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).
Ti→f = (2π/h) |Mif|2 ρf δ(Ef-Ei-ħω)
Ti→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 Ti→f = 1/t
Mfi = <f|Hinteraction|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.
ρf: 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
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« Last Edit: 19.07.12 at 09:08:43 by Gerrit-Jan Linker »  

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