However, in contrast to the usual (single-particle) Schrödinger equation, in which |ψ| is determined by the normalization condition, the Cooper pair condensate density n=|ψ|2 is det...However, in contrast to the usual (single-particle) Schrödinger equation, in which |ψ| is determined by the normalization condition, the Cooper pair condensate density n=|ψ|2 is determined by the thermodynamic balance of the condensate with the ensemble of “normal” (unpaired) electrons, which plays the role of the uncondensed part of the particles in the usual Bose-Einstein condensate – see Sec.
Our derivation makes use of a generalization of the Gaussian integral, ∞∫−∞dxe−12ax2−bx=(2πa)1/2eb2/2a. The general...Our derivation makes use of a generalization of the Gaussian integral, ∞∫−∞dxe−12ax2−bx=(2πa)1/2eb2/2a. The generalization is \[\int\limits_{-\infty}^\infty\!\!\!dx\ns_1\cdots\!\!\!\int\limits_{-\infty}^\infty\!\!\!dx\ns_N\> e^{-{1\over 2} A\ns_{ij} x\ns_ix\ns_j - b\ns_i x\ns_i}={(2\pi)^{N/2}\over \sqrt \ e^\Tra \bigg[e^\!\!\int\limits_{-\infty}^\infty\!\!\!d\phi\ns_1 \cdots\!\!\!\int\limits_{-\infty}^\infty\!\…
