QM: Finite square well with V>0

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Homework Help Overview

The discussion revolves around the concept of bound states in quantum mechanics, specifically in the context of a finite square well with a positive potential (V > 0). Participants are exploring the implications of this scenario on the existence of bound states, contrasting it with the more commonly discussed case of scattering states.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the nature of potential wells versus barriers and the conditions necessary for bound states to exist. There is a focus on the relationship between potential energy and total energy in determining the possibility of bound states.

Discussion Status

The discussion is active, with participants clarifying definitions and exploring the implications of potential energy being positive. Some guidance has been offered regarding the conditions for bound states, but there is no explicit consensus on the formal proof or reasoning behind the absence of bound states in this scenario.

Contextual Notes

There is an underlying assumption that bound states require negative total energy, which is being examined in light of the positive potential scenario. Participants are also referencing standard texts, indicating a reliance on established quantum mechanics principles.

Niles
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Homework Statement


Hi all.

When talking about the finite square well with a potential V > 0 for - A < x < A, I have never seen an example of bound states (i.e. E<0). They only treat examles with scattering states (i.e. E>0). Is there any reason for this? My book (Griffith's Intro. to QM) does not talk about this scenario.
 
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If V>0, then this is not a square well, but a square barrier. Bound states do not exist in this situation.
 
Ahh yes, barrier - not well! Why is that?
 
A well is when V<0, so the particle can "fall in". A barrier is V>0, so there's an obstacle. I'm not sure about a formal proof, but it is hard to imagine a particle bound to a wall. Total energy must be negative somewhere if there is to be a bound state, but kinetic energy is always positive, plus positive potential = no bound state.
 
Can one use the explanation that the energy E always has to be larger than the minimum potential?
 

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