Connection Between Time-Independent Perturbation Theory and Spectroscopic Selection Rules

12-10 Connection Between Time-Independent Perturbation Theory and Spectroscopic Selection Rules 

Molecules may change to higher-or lower-energy states under the influence of incident light. Such processes are called, respectively, absorption and induced emission. Perturbation theory can be used to study such transitions induced by an external oscillating electromagnetic field. Here we briefly describe a rather simple connection between selection mles and the perturbation theory we have discussed in this chapter. 

Let a molecule initially be in a state with wavefunction i/r,. We are interested in the probability of a transition occurring to some final state with wavefunction f. h time-dependent perturbation treatment (not given here, but see Section 6-16) indicates that such a transition is probable only when the external field frequency v satisfies the conservation of energy relation 

Even when this condition is satisfied, however, we may find experimentally that the transition is so improbable as to be undetectable. Evidently some factor other than satisfaction of Eq. (12-86) is also involved. 

At a later time, when the perturbation is over, the system returns to an unperturbed state. The probability of returning to the initial state is given by c c,-. The probability of going instead to the final state described by is given by c c/. If c/ is zero, there 

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