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Please help me to understand the following question:

I have slowly changing electric field that has a zero limits at t1=(- infinity) and t2=(+ infinity). All books write that the time dependant solution is sought in form of linear combination of static eigenfunctions solved at t=(- infinity) with coefficients depending on time. And the probability that system will have n-th eugenvalue will be proportional to square of n-th coefficient. But the last one is true only at t2=(+ infinity) when the field will be zero again and the system of eugenfunctions is unperturbed. At any intermediate time there will be nonzero field and another system of eigenfunctions and eugenvalues. I need to find the probabilities of these perturbed states with its perturbed eugenvalues but I have solution, constructed of nonperturbed functions at any time. I do not understand how to find it. Could you please explain me as for stupid guy? Thanks.

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# Time depending quantum solution

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