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

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The discussion centers on the concept of degeneracy in one-dimensional quantum systems with distant delta potential barriers. It questions how degeneracy can exist for bound states when traditionally, one-dimensional problems do not exhibit this property. The argument suggests that if two identical delta functions are far apart, a particle can be effectively localized to either potential, leading to a form of degeneracy due to equivalent energy states. This raises the idea of treating the system as two separate entities despite being in one dimension. The conversation highlights the complexity of quantum mechanics and references additional resources for further exploration.
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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