Double delta potential -- Degeneracy of bound states in one dimension?

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Discussion Overview

The discussion revolves around the concept of degeneracy of bound states in one-dimensional quantum systems, specifically in the context of double delta potentials that are widely separated. Participants explore the implications of this setup as presented in a lecture by Balakrishnan.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the assertion made in the lecture that distant delta barriers lead to degeneracy, noting that typically in one-dimensional problems, bound states do not exhibit degeneracy.
  • Another participant suggests that if two identical delta functions are far apart, a particle can be approximated as being in either potential, leading to the conclusion that the system is degenerate due to the identical energy levels.
  • A third participant seeks clarification on whether this scenario can be treated as two separate systems, given the usual absence of degeneracy in one-dimensional bound states.
  • A fourth participant provides a reference to a book that may contain relevant information, though it does not directly address the questions raised.

Areas of Agreement / Disagreement

Participants express differing views on the existence of degeneracy in this context, with no consensus reached regarding the implications of the distant delta potentials on bound states in one dimension.

Contextual Notes

The discussion does not resolve the assumptions regarding the nature of bound states and degeneracy in one-dimensional quantum mechanics, nor does it clarify the mathematical treatment of the delta potentials.

LagrangeEuler
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I have a question from the youtube lecture

That part starts after 42 minutes and 47 seconds.
Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.
 
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If I have two identical delta functions very far away and one particle, to a very good approximation it is either in potential #1 or in potential #2. They have the same energy (to an even better approximation) so the system is degenerate.
 
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So if I understand you well it is practical like two separate systems? Because of how to comment on this in the context of that in the one-dimensional problems there is no degeneration in the case of bond states.
 

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