Orbitals while transitioning from free electron to ground state

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Discussion Overview

The discussion revolves around the visualization of electron orbitals as they transition from unbounded or weakly bounded states to the ground state. Participants explore the nature of orbital symmetry, the existence of bound states, and the implications of different potential models.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the probability distribution of orbitals must become asymmetric as it approaches a point, questioning what might be missing in this understanding.
  • Another participant asserts that the Coulomb potential has an infinite number of bound states, implying that a transition from unbound to bound states is not applicable.
  • A participant challenges the assumption that all atomic hydrogen orbitals are spherically symmetric, noting that there are various types of orbitals beyond just s orbitals.
  • One participant explains that recombination emission allows for a transition from unbound to bound states, emphasizing that the shapes of orbitals can be complex and involve superpositions of different states.
  • Another participant reiterates the possibility of transitioning from unbound to bound states, indicating a misunderstanding of the original question posed by the OP.
  • It is noted that sticking to a simple Coulomb potential model may not capture the complexities of real systems, suggesting that models in condensed matter physics might be more relevant.

Areas of Agreement / Disagreement

Participants express differing views on the transition from unbound to bound states, with some asserting it is possible while others argue against it. There is no consensus on the implications of orbital symmetry and the applicability of different potential models.

Contextual Notes

Limitations include assumptions about the symmetry of wave functions in central potentials and the potential applicability of more complex models in condensed matter physics, which remain unresolved.

rconde01
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I was thinking of putting together a visualization of electron orbitals as it transitions from unbounded or weakly bounded state to the ground state. However, it occurred to me that orbitals are symmetric about the proton. At some point the probability distribution must become asymmetric eventually approaching a point. What am I missing?
 
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The Coulomb potential always has an infinite number of bound states however weak you chose the central charge. So there won't be a transition from unbound to bound.
 
Dr. Du, of course you can transition from unbound to bound. This is called recombination emission.

The "s", "p", "d", "f"... orbitals are just one way of representing the state, which can have almost arbitrary shape of the electron distribution. The arbitrary shape will be some superposition of orbitals. It is analogous to how an arbitrary wave is a superposition of frequency components. Just as a localized wave-packet doesn't have a single frequency, a localized electron doesn't have a single orbital state.

A weakly bounded atom is called a Rydberg atom. http://en.wikipedia.org/wiki/Rydberg_atom
This is a case where a classical representation (planetary model) of an atom can be useful. The corresponding quantum state is some kind of coherent state of the Rydberg atom which mixes angular momentum states.

You might be able to find something by searching for coherent states of Rydberg atom. Good luck. It's not an easy problem. I'm interested in how the results look.
 
Khashishi said:
Dr. Du, of course you can transition from unbound to bound. This is called recombination emission.
Of course. Apparently I was thinking in something completely different to what the OP was asking.
 
It occurs to me if you stick to the simple model of Couloumb potential you are never going to do so. Since central potential has parity symmetry, which means the wave functions chosen are always symmetric or antisymmetric... I think for the more realistic situation, models in condensed matter might be more applicable.
 

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