What is the criteria for bound states

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Discussion Overview

The discussion revolves around the criteria for bound states in quantum mechanics, particularly in the context of the hydrogen atom. Participants explore the nature of binding energy, its calculation, and the distinction between bound states and other forms of energy interactions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants reference the Wikipedia article on bound states but express confusion regarding the specific energies of the electron in hydrogen, suggesting these are special cases rather than general relations.
  • One participant states that bound states cannot have enough energy to fall apart, prompting questions about whether this refers to potential or kinetic energy.
  • Another participant clarifies that the total energy is what matters for determining binding energy, indicating that the calculation of binding energy is system-dependent.
  • A participant questions what makes binding energy unique compared to other interaction energies, suggesting that the uniqueness lies in the terminology used.
  • It is noted that solving Schrödinger's equation for a potential that vanishes at infinity leads to the identification of bound states as those eigenstates that vanish at infinity.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and definition of binding energy and its calculation, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Limitations include the lack of consensus on the definitions of potential and kinetic energy in the context of binding energy, as well as the specific conditions under which binding energy is calculated.

ftr
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I read this wiki and some of the references
https://en.wikipedia.org/wiki/Bound_state

But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.

Thanks
 
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ftr said:
For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.
The specific energies of hydrogen are special cases.

What is unclear?
 
mfb said:
What is unclear?

What is the criteria for bound states?
 
They can't have enough energy to fall apart.
 
mfb said:
They can't have enough energy to fall apart.
Ok thanks. But I am still not clear, do you mean potential or kinetic, and how is the binding energy calculated from them.

edit: It also seems to be potential specific as in this paper
https://arxiv.org/pdf/hep-ph/0407258.pdf
 
I mean the total energy.

How to calculate the binding energy of a specific system depends on that system.
 
mfb said:
How to calculate the binding energy of a specific system depends on that system.

I guess my question is again what makes this binding energy unique as opposed to any other interaction energy that may arise.
 
ftr said:
I guess my question is again what makes this binding energy unique as opposed to any other interaction energy that may arise.
The only thing that's unique about it is that we've decided to call it "binding energy".

If you solve Schrödinger's equation for a potential that vanishes at infinity, you will find that some of the eigenstates vanish at infinity and some do not. We call the ones that do vanish at infinity "bound states", and we call their energy eigenvalues "binding energy".
 

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