Recently Eliashberg derived the theory of superconductivity by the Green's function technique. The energy-gap equation was deduced by a self-consistent calculation. The result is similar to the integral equation of Bardeen, Cooper, and Schrieffer except that the effective electron interaction potential is different from the Bardeen-Pines potential as well as the Bogoliubov potential. The purpose of this paper is to discuss these differences. It shows that the "dangerous terms" in the Bogoliubov theory may be calculated in a different manner. The compensation of these dangerous terms leads to the result of Eliashberg. Therefore the self-consistent calculation of Eliashberg is but a different interpretation of the Bogoliubov's idea. However, it is argued that the most reliable way of treating the problem should be the variational method because it gives the lowest ground-state energy. This method gives all the results of Bogoliubov in the lowest order of approximation, but is free from arbitrary interpretations.

• Received 20 September 1961

DOI:https://doi.org/10.1103/PhysRev.125.1244