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I wouldn't so casually dismiss BCS theory. BCS contains one of only a few exactly solvable wave functions. It's used in everything from superconductivity to neutron stars. Actually, anytime there is a fermi sea instability BCS is a good starting framework. It's an triumph of modern physics.

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There’s a reason I call the BCS theory “seductive”. It’s striking, beautiful and powerful. I also think it’s clear that BCS is far from the whole story when it comes to superconductivity and I also think the huge success of the BCS theory has cast a long shadow which makes developments in different directions more difficult.

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