Time-independent perturbation and the Fermi golden rule

3 TIME-INDEPENDENT PERTURBATION AND THE FERMI GOLDEN RULE 

Now let us calculate the probability density Pj = cic P, that at time t the system will be in state k (the initial state is m)  

As one can see, is proportional to time t, which makes sense only because T has to be relatively small (first-order perturbation theory has to be valid). Note that the Dirac delta function forces the energies of both states (the initial and the final) to be equal, because of the time-independence of V. 

A iime-maepenaeni periuroation is unaoie to cnange me state or me system when it corresponds to a change of its energy. 

A very similar formula is systematically derived in several important cases. Probably this is why the probability per unit time is called, poetically, the Fermi golden rule  

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Time-Independent Perturbation and the Fermi Golden Rule... 

Time-independent perturbation and the Fermi golden rule... 

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