= Fermion number of a Bogoliubov excitation
{title2=$\Delta\langle N\rangle=\epsilon/E$}
For a normalized spinless paired <ground state> $u|0\rangle+i v c_p^\dagger c_{-p}^\dagger|0\rangle$, its mean <fermion number> is $2v^2$. The canonical <Bogoliubov quasiparticle> <creation operator> produces $c_p^\dagger|0\rangle$, containing exactly one fermion. With <BCS coherence factors> $v^2=(1-\epsilon/E)/2$, the change in mean <fermion number> is $1-2v^2=\epsilon/E$. This need not be an integer because the pairing <Hamiltonian> preserves <fermion parity> while failing to conserve the original <fermion number operator>. Every measurement of that <number operator> still has integer outcomes.
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