An analytic solution to the BCS equation for the superconducting transition temperature has been obtained. Instead of the electron- phonon interaction being assumed to be a constant in a certain range as was done in BCS theory, it has been considered varying with energy, a case more physical in nature. The resulting equation for the superconducting transition temperature Tcreduces to the standard BCS form when Tcis small but this equation does not put any higher limit on Tc. The gap parameter at the absolute zero has also been analytically obtained. These equations have been successfully applied to the high temperature superconductors. © 1992.
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