Transition from bound states to continuous states

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Discussion Overview

The discussion revolves around the transition from bound states to continuous states in quantum mechanics, specifically in the context of the Hydrogen atom under the influence of a classical electric field. Participants explore the implications of perturbation theory and the conditions necessary for such transitions to occur.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether a transition from a bound state to a continuous state is possible, noting that their calculated probability amplitude using the Dyson series is zero.
  • Another participant acknowledges the physical possibility of ionizing an atom, suggesting that it is feasible to transition an electron from a bound state to a scattering state.
  • A request is made for the original poster to share their calculations to identify any potential errors in their approach.
  • A participant raises a point about the importance of conserving angular momentum during the transition process.
  • The original poster later indicates that they resolved their issue, attributing it to a calculation mistake.

Areas of Agreement / Disagreement

The discussion reflects a mix of uncertainty and exploration, with some participants questioning the conditions for transitions while others affirm the physical possibility of such processes. The original poster's eventual resolution of their issue does not imply consensus on the broader topic.

Contextual Notes

Limitations include the need for clarity on the assumptions made in the calculations and the specific conditions under which the transitions are considered. The discussion does not resolve the broader implications of the transition from bound to continuous states.

giova7_89
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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 |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..
 


giova7_89 said:
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.
 


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


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

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