Coordinates, spatial and spin

Suppose that we want to calculate the probability density that two electrons with the same spin coordinate or are in the same place (Le., that these two electrons have all their coordinates, spatial and spin ones, identical). If so, then the two columns of the abovementioned determinant are identical. And this means that the determinant becomes equal to zero. From this, and from the continuity of the wave function, we may conclude that... 

Note that in Eq. [4], the integration is carried out over all coordinates (spatial and spin) of the electrons 2 to N, and over the spin only for the first electron. 

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See also in sourсe #XX -- [ ]

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