Sinusoidal drive of two level system: why can we ignore one of the two terms? I am studying the time-dependent perturbation theory from Griffith's Introduction to Quantum Mechanics. The context is a two-level system under a sinusoidal perturbation: $H'(\textbf{r}, t) = V(\textbf{r}) \cos(\omega t)$, where the symbols have their usual meanings. 
He gets the following expression (eq. (9.25)): 
$$c_b(t) = -\frac{V_{ba}}{2\hbar} \left[ \frac{e^{i(\omega_0+\omega)t} - 1}{\omega_0+\omega} + \frac{e^{i(\omega_0-\omega)t} - 1}{\omega_0-\omega} \right].$$
For $\omega_0+\omega \gg |\omega_0-\omega|$, he says that the second term in the square brackets dominates.
How do we know that the second term in the square brackets dominates from the condition $\omega_0+\omega \gg |\omega_0-\omega|$ ?
 A: As mentioned in the comments, this is known as the Rotating-Wave Approximation, and it holds because the exponents $(\omega\pm \omega_0)t$ are real, so that the exponentials $|e^{i(\omega\pm \omega_0)t}|\leq 1$ are bounded in modulus, so that 
$$
\omega_0+\omega \gg |\omega_0-\omega|
\implies
\frac{1}{\omega_0+\omega} \ll \left|\frac{1}{\omega_0-\omega}\right|
$$
and the exponentials don't change the picture much.
However, while we're here, it's important to note that there's a wide array of important real-world situations where the RWA can fail to capture important parts of the physics. It's a great tool, and much of the time you can build enormous theoretical edifices within its confines while keeping excellent agreement with experiment, but it can indeed break. (Though countering that, as Peter Knight once said, if you're looking to study physics beyond the RWA, you'd better think carefully about whether there are other approximations which will break before it and which you should investigate first.)
