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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.