Ionizing solutions to the hydrogen atom

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SUMMARY

Ionizing solutions for the hydrogen atom problem exist, specifically for energy levels greater than zero (E > 0), which correspond to a continuum of unbound states. This is analogous to a particle in a finite-barrier box where E > V. The transition from a bound state to an unbound state is fundamentally similar to transitions between bound states. For a comprehensive understanding of these solutions, refer to "Quantum Mechanics" by Landau and Lifshitz, which discusses continuum eigenstates of the hydrogen atom in detail.

PREREQUISITES
  • Understanding of the time-dependent Schrödinger equation
  • Familiarity with quantum mechanics concepts, particularly bound and unbound states
  • Knowledge of continuum eigenstates in quantum systems
  • Basic principles of particle behavior in potential barriers
NEXT STEPS
  • Study the time-dependent Schrödinger equation in detail
  • Explore continuum eigenstates in quantum mechanics
  • Research ionization processes in quantum systems
  • Read "Quantum Mechanics" by Landau and Lifshitz for advanced insights
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Students and professionals in quantum mechanics, physicists studying atomic interactions, and anyone interested in the ionization of hydrogen atoms.

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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