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A time varying Hamiltonian H(t) induces transitions from state |k> at time t=0 to a state |j> at time t=t' with probability P(k to j(t')). Use first order time-dependent peturbation theory to show that if P(j to k(t')) is the prababilty that the same Hamiltonian brings about the transition from state |j> to state |k> in the same time interval, then P(k to j(t')) = P(j to k(t')).

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# Probability in first order time-dependent perturbation theory

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