Solution
= Solution
First-order <time-dependent perturbation theory> gives
$$
c_1(t)=-{i\over\hbar}\int_0^t e^{i(ω_1-ω_0)t\prime}\langle1|V(t\prime)|0\rangle\,dt\prime.
$$
The lowest nontrivial transition probability is $|c_1(t)|^2$, with errors of higher order in $V$.