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This scalar product appeared long ago in the equation (4.2) of the Blatt's book, Theory of Superconductivity, Academic Press, N.Y. (1964). The result written in this book is however incorrect because it is not unchanged under the (i↔j) or (m↔n) permutations, as it should
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This relation has already been found by Girardeau as equation (58) in reference 4
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