  We investigate the condensate density and the condensate fraction of
conduction electrons in weak-coupling superconductors by using the BCS theory
and the concept of off-diagonal-long-range-order. We discuss the analytical
formula of the zero-temperature condensate density of Cooper pairs as a
function of Debye frequency and energy gap, and calculate the condensate
fraction for some metals. We study the density of Cooper pairs also at finite
temperature showing its connection with the gap order parameter and the effects
of the electron-phonon coupling. Finally, we analyze similarities and
differences between superconductors and ultracold Fermi atoms in the
determination of their condensate density by using the BCS theory.
