Fermi’s Golden Rule formula

Note that the results derived from this definition are equivalent to those derived from Fermi s golden rule [23]. Hence we refer to them as a Fermi s golden rule formula. 

As the bright state mixes with more and more dark states, the resultant lineshape evolves toward a smooth Lorentzian shape (Bixon and Jortner, 1968). The width of this composite line approaches that predicted by Fermi s Golden rule formula... 

This formula, first obtained by Dirac, is commonly known as Fermi s Golden Rule (FGR). 

This formula of the time-dependent perturbation theory was originally derived by Dirac, but it is often referred to as Fermi s golden rule No. 2. ... 

The expression for the rate R (sec ) of photon absorption due to coupling V beriveen a molecule s electronic and nuclear charges and an electromagnetic field is given through first order in perturbation theory by the well known Wentzel Fermi golden rule formula (7,8) ... 

The interpretation of Eq. (4-3) is direct and the formula could almost be written down immediately in terms of Fermi s familiar Golden Rule of quantum theory (see, for example, Schiff, 1968, p. 314). The absorption of light arises from the coupling, caused by the electric field, of occupied states with unoccupied states, However the absorption can only occur if the two states differ in energy by hco, so that energy can be conserved if the transition is made and one photon is absorbed. It should also be noted that in a perfect crystal the matrix elements will vanish unless the wave numbers of the coupled states in the Brillouin Zone are the same. That is, the transitions must be between states that are on the same vertical line in a diagram such as Fig. 4-7. We shall return to a more complete description of absorption later. 

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