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**Transition from bound states to "continuous" states**

If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a discrete state [tex]|n,l,m>[/tex]) to a state with energy greater than 0 (that is a state in the continuous spectrum of the unperturbed Hamiltonian). I calculated the probability amplitude [tex]<E|n,l,m>_t[/tex] by means of the Dyson series and it comes off as 0...