Quasiadiabatic solution to the two-level problem

We consider a two-level system where a pair of discrete quantum states of arbitrary widths and separation are coupled by a general time-dependent external field with a pulselike matrix element, $V\left(t\right)\mathrm{}$. Using a transformation suggested by Robinson [Phys. Rev. A 24, 2239 (1981)] and applying the WKB approximation, a quasiadiabatic solution is constructed for the system's transition amplitude. This solution is useful in estimating transition amplitudes in the asymptotic region for a wide variety of smoothly varying pulses $V\left(t\right)\mathrm{}$.