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My question is, is there any physical intuition explaining why this is the case? Before solving this problem, I thought that since there are two delta wells, there will be two bound states, but this is not always the case.

For example, if I have two electrons, and my α is large enough to admit two bound states, I assume that I can place each electron into a well.

If however, α is small such that there can be only one bound state, then does this mean that I can only put one electron into a well, and the other well must be empty?

I appreciate any insight!