What is excursion of a potential well?

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Discussion Overview

The discussion revolves around the term "excursion" in the context of potential wells, particularly in quantum mechanics. Participants are trying to clarify its meaning and its relation to the Schrödinger Equation, specifically in a spectral method context.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that "excursion" refers to the maximum depth of the potential well, although they express uncertainty due to their limited background in quantum mechanics.
  • Another participant interprets "excursion" as the difference between the maximum and minimum values of the potential, indicating a possible definition.
  • Some participants agree with the interpretation of "maximum excursion" as max(V) - min(V), but they express confusion because the numbers provided in the referenced paper do not align with this interpretation.
  • A participant raises the possibility of a typo in the referenced paper, suggesting that it could lead to the confusion experienced by others.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of "excursion" as related to the maximum and minimum of the potential, but there is disagreement regarding the accuracy of the referenced paper and its implications for their understanding.

Contextual Notes

Participants note that their interpretations are based on the definitions they assume, and there is uncertainty regarding the relationship between the maximum depth of a potential well and the bandwidth of the energy spectrum.

rcompton
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What is "excursion" of a potential well?

I think it means maximum depth of the well, but I've never heard this term before and I might be wrong. I don't have much of a quantum mechanics background.

Details:
I'm reading and implementing "Solution of the Schrödinger Equation by a Spectral Method" by Feit et al. They refer to delta_V as the "maximum excursion" of the potential. I interpret this to mean "minimum" of the potential, but my interpretation does not match up with the numbers they provide at the end.

EDIT: If someone could just give me the relation between the maximum depth of a potential well and the bandwidth of the energy spectrum that would solve it for me.

EDIT2: Time independent Hamiltonian.
 
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My offhand interpretation would be to assume it was the difference between the maximum and the minimum of V.
 


Yeah, that's what I think as well. But it's not lining up so I'm confused.
 


Yeah, it looks like "maximum excursion" means max(V) - min(V). They must have a typo in their paper, which is upsetting as it's J comp. physics and has ~1000 citations.
 

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