# Transition from bound states to continuous states

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 $$|n,l,m>$$) 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 $$<E|n,l,m>_t$$ by means of the Dyson series and it comes off as 0...

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And what bothers me is that I know that is physically possible to ionize an atom... That is, send an electron in a bound state into a scattering state..

A. Neumaier
2019 Award

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 $$|n,l,m>$$) 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 $$<E|n,l,m>_t$$ by means of the Dyson series and it comes off as 0...
Maybe you should share your calculation. Otherwise one cannot tell what you did wrong.

Matterwave