QM: The double square well potential

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QM: The "double square well" potential

Homework Statement



Consider the "double square well" potential below. Qualitively (no calculations) how do the energies of the ground state and the first excited state vary as b goes from zero to infinity (i.e. the two wells become further and further apart)?

[PLAIN]http://img12.imageshack.us/img12/9164/unlednpw.jpg [Broken]


The Attempt at a Solution



I've worked out the energy levels of the finite square well in a previous question, so the energies in this case should revert back to those for b=0. It is for when b goes to infinity which I need help.

We'll end up with two isolated square wells of width a, for which I know the individual allowed energies, but how do these combine to give the overall energy? In the ground state of the system would both the individual square wells be in their ground state? Then in the first excited state of the system, would one of the individual square wells be in its first excited state whilst the other is still in its ground state? But then it's like you've got 2 different energies for one state, so this is probably wrong :\

Thanks for any help :-)
 
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Anyone? :-(
 

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