Probability of transition in hydrogen atom

[mathlete]

Here's the question...

A hydrogen atom is in the ground state at time t = 0. At this time an external electric field of magnitude E(t)=E*exp(-t/tau) is applied along the z direction. Find the first-order probability that the atom will be in the 210 (nlm) state at time t >> tau, assuming that the spontaneous transition probability for the 2p -> 1s transition is negligible at that time.

What I'm thinking is I need to find the average pertubation (<psi|H'|psi>) and then use time dependent pertubation theory to solve this... but I'm not really sure what wave functions i'd use to do this. But also I'm conflicted if I should really be doing it this way and not using something for absorption/stimulation in the electric dipole approximation... any suggestions?

 

[Physics Monkey]

Hi mathlete,

This is straight time dependent perturbation theory. You need to calculate the amplitude c_{f i} to go from the initial state i to the final state f. Your book will certainly contain the relevant formulae, but basically you know that the amplitude is proportional to the matrix element of the perturbation between the initial and final states with some integral that captures the time depedence.

Hope this helps.