Abstract
The electron-pair density matrix \gr(k 1, k 2; k 3, k 4, t) =: \gr(1, 2; 3, 4, t) changes in time, following a quantum Liouville equation with in the presence of a Coulomb interaction {itv}{in{itc}}, where \gW is the volume. If the virtual phonon exchange is in action, the density matrix \gr is shown to change similarly with an effective interaction {itv}{in{ite}}, by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.
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