Two-Body Correlation of Interacting Fermions

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Abstract
The electron-pair model, proposed for superconductivity by Bardeen, Cooper and Schrieffer, is discussed in the configuration space. The wave function for the system of electron-pairs is taken as follows, Ψ0 = ∑p(-1)p P{χ(1, 2)χ(3,4)⋯χ(2N-1, 2N)}, where χ(1, 2) is the wave function for the singlet state of a two electron system. By a method having a remarkable similarity to Mayer's theory of an imperfect gas, the expectation value of the system can be obtained rigorously. The expression for energy coincides with that which is given by Bogoliubov in his theory of superconductivity. By a variational method, Bogoliubov's integral equation is obtained.

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