Question about time limits of time-dependent perturbation theory

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SUMMARY

The discussion centers on the application of time-dependent perturbation theory in quantum mechanics, specifically regarding the integration limits for calculating transition amplitudes. Users have observed discrepancies between using limits from 0 to t and from -infinity to t, leading to significantly different results. The consensus indicates that the appropriate limit depends on the context of the perturbation, with the 0 to t limit being more relevant when the perturbed field is only active for a finite duration.

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ani4physics
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I have been using time-dependent perturbation theory for quite a while. Yet, one thing is still not clear to me. I have seen in many books and papers that when they calculate the transition amplitudes, they integrate from 0 to t. While in many other papers and books, the limit is taken to be - infinity to t. Those two limits give completely different results for transition amplitudes and transition probabilities. So which one to use?
 
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I would expect only 0 to t for the time that the perturbed field is switched on.

How can you use a transition amplitude based on an infinite amount of time being exposed to the field?
 

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