Ionizing solutions to the hydrogen atom

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Discussion Overview

The discussion revolves around the existence of ionizing solutions for the hydrogen atom, specifically focusing on scenarios where the electron transitions from a bound state to an unbound state, such as during a collision. The scope includes theoretical aspects of quantum mechanics and the behavior of electrons in atomic systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that for energy levels greater than zero, there exists a continuum of unbound states for the hydrogen atom.
  • There is a suggestion that the transition to an unbound state is not fundamentally different from transitions between bound states.
  • One participant requests specific solutions or references related to the time-dependent Schrödinger equation and ionization processes.
  • A reference to the book by Landau and Lifshitz is provided as a source for understanding continuum eigenstates of the hydrogen atom.

Areas of Agreement / Disagreement

Participants express differing views on the nature of transitions from bound to unbound states, with some asserting similarities to transitions between bound states, while others seek clarification and specific examples. The discussion does not reach a consensus on the specifics of ionizing solutions.

Contextual Notes

There is a lack of detailed examples or solutions presented in the discussion, and the participants' references to literature suggest a dependence on external sources for further exploration of the topic.

mordechai9
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Are there any ionizing solutions for the hydrogen atom problem, where the electron breaks away from the proton?
 
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Of course. For E > 0 you have a continuum of unbound states. Same as for when E > V for a particle in a finite-barrier box.
 
I mean a solution where the electron transitions from being bound to breaking away... like in a collision.
 
And the answer is still "of course".

Why would a transition to an unbound state be fundamentally different than transitions between bound states? It isn't.
 
Could you help point me to one of these solutions then? I don't recall ever seeing the time-dependent Schrödinger equation solved for transitions or ionization and I'm not sure where to look...
 
The book by Landau and Lifshetz "Quantum Mechanics" has a fairly complete discussion of the continuum eigenstates of the hydrogen atom.
 

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