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In superconductors, the fermions are interacting. In order to diagonalize our Hamiltonian (which contains the product of four fermion operators), we use Wick's theorem to approximate the product of four fermion operators by the product of two fermion operators.

Now, a Hamiltonian consisting of the product between two fermion operators describes a non-interacting system. Isn't that a contradiction?

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# BCS Hamiltonian

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