We now assume that $=0.$ In this limit we can ignore the terms in Eq$.3$ that rotate with the frequency $2$ because this is a very fast oscillating term $($on the order of $1015$ Hertz$)$ and averages out very quickly. The terms with $0$ on the other hand do not rotate at all, so they do not average out and we must keep them. Using this approximation, solve for A and B as a function of time assuming the atom is initially in the ground state. Show that the probability of being in the excited state is