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

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SUMMARY

The discussion centers on the concept of degeneracy in bound states within one-dimensional quantum systems, specifically regarding the behavior of distant delta barriers. Balakrishnan's lecture indicates that when delta barriers are sufficiently separated, degeneracy occurs, allowing a particle to be approximated as residing in either potential. This leads to the conclusion that the system behaves similarly to two independent systems, despite the general rule that bound states in one dimension do not exhibit degeneracy. The participant references a resource for further understanding, highlighting the complexity of the topic.

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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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