Chapter 11.1, Problem 11.9P

(a)

To determine

The coefficients $c_a\left(t\right)$ and $c_b\left(t\right)$ in terms of Rabi flopping frequency.

(b)

To determine

The transition probability $P_{a\to b}\left(t\right)$ and show that it never exceeds 1 and confirm that ${\left|c_a\left(t\right)\right|}^2+{\left|c_b\left(t\right)\right|}^2=1$.

(c)

To determine

Check the $P_{a\to b}\left(t\right)$ reduces to the perturbation theory result given in equation 11.35.

(d)

To determine

The time taken by the system to return to its initial state.