We present the explicit forms of the maximum eigenvalue and the corresponding eigenfunction for the second-order reduced density matrix (RDM2) of the BCS superconducting state (SS). Using these quantities, we deal with two topics in the present paper. As the first topic, it is shown that the cluster decomposition principle holds in the BCS-SS. This proof gives a theoretical foundation that the abnormal density can be chosen as the order parameter of the SS. As the second topic, it is shown that such an eigenfunction is spin singlet and spatially extends isotopically, and further that the mean distance of two electrons which consists of the above eigenfunction is in a good agreement with Pippard’s coherence length. This means that maximum geminal of the RDM2 of the BCS-SS can be regarded as the Cooper pair itself which are condensed to the same energy level in a number of

我们提出了 BCS 超导态 (SS) 的二阶约简密度矩阵 (RDM2) 的最大特征值的显式形式和相应的特征函数。使用这些数量，我们在本文中处理两个主题。作为第一个主题，表明簇分解原理在 BCS-SS 中成立。该证明为选择异常密度作为SS的阶参数提供了理论基础。作为第二个主题，证明了这样的本征函数是自旋单线态的，并且在空间上同位素地延伸，而且由上述本征函数组成的两个电子的平均距离与Pippard的相干长度非常吻合。