It'd be great if you could help me clarify a few things in my head. Firstly I've got written in my notes "quantum mechanics forbids spontaneous transitions from one energy level to another because energy eigenfunctions are time independent". However this seems a bit of a circular argument. I was under the impression that all electron wavefunctions are in fact decaying exponentially with time, but instead the probability density is time independent. Is this true? Secondly, I'm willing to accept a spontaneous emission can be induced by vacuum fluctutions, but I'm not too sure what this means. Now the main problem I've got is: during a transition, the atom is in a superposition of 2 states (lets say 2p0 and 1s0 where these represent the quantum number n, l and ml). In my notes I'm told to consider a "50:50" superposition and calculate the distribution at various times. From this I can see that the charge distribution "sloshes" backwards and forwards with time which I appreciate will emit radiation. However, how do you get out of these seemingly eternal oscillations and finally settle down into the ground state? Surely the 50:50 ratio will have to change, so after a certain time it becomes a 0:100 ratio? Am I thinking about this in the correct way? Any help would be appreciated.