Show that a variational calculation with a BCS wavefunction as the variational state, where (hat{H}) is the

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Show that a variational calculation with a BCS wavefunction as the variational state,

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where \(\hat{H}\) is the Hamiltonian and \(\lambda\) is the variational parameter, leads to \(\lambda=d E / d N\), where \(E\) is the energy and \(N\) is the average particle number.

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