What is excursion of a potential well?

In summary, "excursion" of a potential well refers to the maximum depth of the well. However, the term may also be used to describe the difference between the maximum and minimum values of the potential. This term is used in the context of quantum mechanics, specifically in the solution of the Schrodinger Equation. There may be some inconsistencies in the use of this term, as different interpretations have been observed in the literature.
  • #1
rcompton
9
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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 Schrodinger 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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  • #2


My offhand interpretation would be to assume it was the difference between the maximum and the minimum of V.
 
  • #3


Yeah, that's what I think as well. But it's not lining up so I'm confused.
 
  • #4


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.
 

FAQ: What is excursion of a potential well?

What is the excursion of a potential well?

The excursion of a potential well refers to the distance between the bottom of the well and the point where the potential energy becomes zero. It is a measure of the depth of the potential well.

Why is the excursion of a potential well important in physics?

The excursion of a potential well is important in physics because it determines the stability and behavior of particles within the well. A shallow potential well will allow particles to easily escape, while a deep potential well will trap particles inside.

3. How is the excursion of a potential well calculated?

The excursion of a potential well can be calculated by finding the difference between the potential energy at the bottom of the well and the point where the potential energy becomes zero. This can be done using mathematical equations or by graphing the potential energy curve.

4. Can the excursion of a potential well change?

Yes, the excursion of a potential well can change depending on factors such as the strength of the potential energy and the position of the particle within the well. It can also be affected by outside forces such as temperature or pressure.

5. What is the relationship between the excursion of a potential well and the stability of a system?

The excursion of a potential well is directly related to the stability of a system. A larger excursion means a deeper potential well, which results in a more stable system. A smaller excursion indicates a shallower potential well, which can lead to a less stable system that is more likely to undergo changes or fluctuations.

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