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We present the explicit forms of the maximum eigenvalue and the correspondingeigenfunction for the second-order reduced density matrix (RDM2) of the BCSsuperconducting state (SS). Using these quantities, we deal with two topics inthe present paper. As the first topic, it is shown that the clusterdecomposition principle holds in the BCS-SS. This proof gives a theoreticalfoundation that the abnormal density can be chosen as the order parameter ofthe SS. As the second topic, it is shown that such an eigenfunction is spinsinglet and spatially extends isotopically, and further that the mean distanceof two electrons which consists of the above eigenfunction is in a goodagreement with Pippard's coherence length. This means that maximum geminal ofthe RDM2 of the BCS-SS can be regarded as the Cooper pair itself which arecondensed to the same energy level in a number of O(N).

Cluster Decomposition Principle and Two-Electron Wave Function of the Cooper Pair in the BCS Superconducting State