FROM BCS THEORY FOR ISOTROPIC HOMOGENEOUS SYSTEMS TO THE COMPLETE GINZBURG-LANDAU EQUATIONS FOR ANISOTROPIC INHOMOGENEOUS SYSTEMS

On the basis of the BCS theory of superconductivity, this paper gives the complete expression for the free-energy density F-s as a function of the superconducting energy gap Delta(T) and temperature T, valid fo r the entire superconducting temperature range. Then under the conditi on Delta(T)/kT<1, the complete expansion of the phenomenological Ginzb urg-Landau free-energy density is derived from the BCS free-energy den sity. For isotropic inhomogeneous systems and systems in magnetic fiel ds, the complete expansions of these two kinds of free energy and the relations between the microscopic and phenomenological coefficients ha ve been determined. Complete forms of the Ginzburg-Landau equations ar e obtained for both isotropic and anisotropic systems. Finally, we hav e found the nonlinear equation of the energy gap and the expression fo r the current density for anisotropic inhomogeneous systems within the framework of BCS theory. The range of validity of these equations is extended to Delta(T)/pi k<T less than or equal to T-c rather than the usual T-->T-c.