Population control of 2s-2p transitions in hydrogen

We consider the time evolution of the occupation probabilities for the 2s-2p transition in a hydrogen atom interacting with an external field V(t). A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Schroedinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.