I'm studying the hydrogen atom and have this question. Apparently it can be solved without perturbation theory, however I'm having trouble justifying it. 1. The problem statement, all variables and given/known data 2. The attempt at a solution Avoiding perturbation theory I simply get: E = E(n) - constant*(mh) where m is the angular momentum number not mass Which seems a little too easy. For the second part I can see the initial t=0 wavefunction is normalised no problem, but when I apply the time evolution operator e^(iEt)/h things get messy. Am I right in thinking the probability for the third state | 2 1 0 > is just zero for all time?