Transition from bound states to continuous states

[giova7_89]

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...

 

[giova7_89]

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]

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]

Did you make sure to conserve angular momentum in your transition?

 

[giova7_89]

Thank you but I managed to solve my problem. It was a calculation mistake!